Definitional Issues And Applicable Law
There are some definitional issues here.
There are three classes of offenses for which corporal punishment are authorized in Iran under Shia Islamic law. See also here.
You are referring to Qisas (the law of retaliation/retribution) which is a private individual right to demand retribution punishment including corporate punishment from another private individual, instead of Diyyeh (blood money) under the Qanon-e Qisas (Retribution Law) enacted in 1982.
Corporal punishment for overlapping conduct is also authorized for Hadd crimes (offenses against God) (applied directly under mandatory Koranic language), and Tazir (deterrent crimes) authorized by the Qanon-e Ta'zir (Discretionary Punishment Law) enacted in 1982. Hadd crime sentences are not commonly implemented (at least in full) due to the high burden of proof and the emphasis on repentance and forgiveness required. Most criminals thus receive a lesser conviction, through the tazir code (tazir sentences frequently involve up to 99 lashes and for certain repeated serious drug related crimes, for treason and for espionage, for example, the death penalty, but rarely amputation type punishments).
While these are separate and distinct bases for the imposition of corporal punishment, distinguishing the actual legal basis of a corporal punishment, given that the factual circumstances that justify each basis overlap significantly, is not easy without access to official Iranian records, and there is a serious risk of mistranslation of these subtleties in non-official reporting. It is not clear how important these distinctions are to the question being asked.
These laws have sense been recodified including some reforms since 1982:
In 1991–1994, Iran combined all of these laws into the unified
"Islamic Penal Code" which consisted of five "Books". The new Islamic
Penal Code was adopted in January 2012 and incorporates the bulk of
penal laws in the IRI, replacing Books One through Four of the old
code. Book Five of the Islamic Penal Code ("the only part of the Penal
Code that has been adopted permanently and is not subject to
experimental periods") passed on May 22, 1996. Book Five deals with
ta'zir crimes and deterrent punishments, crimes against national
security, crimes against property, against people, theft, fraud,
forgery, insult and many other offenses.
In 2012, the authorities said that qisas would not be applied anymore
for youths under 18 years of age, except in rare cases. However, Iran
uses the lunar Islamic calendar to determine criminal age, meaning
some "eighteen-year olds" would actually still be seventeen years old.
. . . Qisas cannot be applied in cases of self-defense, manslaughter,
where the case lacks the proof requirements, on minors (age 15 for
boys, 9 for girls prior to 2012, after 2012 aged 18 in most cases), on
insane people, a person who murdered a spouse and/or their lover
caught in the act of adultery, a father who murders his children, etc.
There have been other recent reforms limiting the death penalty in Iran, which while not strictly on point, tend to show the tendency of the system as a whole according to this report from 2019:
According to rights groups, Iran executed at least 225 as of November
9, compared to 507 in 2017.
The decrease in number is largely due to an amendment to Iran’s drug
law that went into force in November 2017. Since November 2017, the
judiciary has halted most executions of individuals convicted of drug
offenses in order to review their cases in accordance with an
amendment to Iran’s drug law that raised the bar for imposing
mandatory death sentences. On January 15, Hassan Norouzi, the
parliamentary judicial spokesperson, told domestic media that
authorities are reviewing some 15,000 cases as part of this process.
However, rights organizations have since documented four executions
related to drug offenses and armed robbery.
The judiciary also executed at least five individuals who were
sentenced to death for crimes they allegedly committed as children.
Under Iran’s current penal code, which went into force in 2013, judges
can use their discretion not to sentence individuals who committed the
alleged crime as children to death. However, several individuals who
were retried under the new code for crimes they allegedly committed as
children have been sentenced to death again.
The same report notes that there are only 20 lawyers in the country authorized to serve as criminal defense lawyers in national security cases, which suggests an order of magnitude estimate for the maximum number of such cases.
It isn't easy to know what proportion of executions are for which of the three possible categories of crimes that could authorize them, except that drug crime executions are for Tazir and prior to 2018 apparently accounted for about half of all executions in Iran.
Data On Imposition Rates
The U.S. State Department takes the position that some "judicially sanctioned corporal punishment constituted cruel and inhuman punishment" and reports upon that non-systemically as cases are brought to its attention as human rights violations in its regular human rights reports about Iran. See, e.g. this 2011 report. So, these punishments are definitely applied officially, multiple times a year (which news reports confirm).
There is good data on the rate at which the death penalty is applied in Iran (although perhaps not perfect). Iran has the highest execution rate in the world, other than China. And, since the death penalty in Iran is part of a comprehensive lex talonis system applying Islamic law, and Iran has one of the highest rates of application of the death penalty of countries that conduct Islamic law capital punishment (additional statistics available here), it is a fair assumption that lesser instances of corporal punishment than death are likewise applied in Iran at higher rates than most other countries that recognize corporal punishments authorized by Islamic law as a legal possibility.
On the other hand, an upper limit can be inferred from the fact that the officially reported crime rates for conduct for which these punishments are authorized is fairly low by international standards in Iran (e.g. the homicide rate in Iran is about 2.5 per 100,000 people compared to 5.0 per 100,000 in the U.S.) (Iran had a population of 81.8 million people in 2018 while the U.S. had a population of 327.2 million in 2018). Crimes involving guns are about 12 times less common in Iran than in the U.S.
Anecdotal reports are unequivocal and uniform in reporting the corporal punishment is actually imposed in a small fraction of the cases in which Sharia law would naively appear to authorize it and that mercy is granted in a very large share of cases where retributive corporal punishment is authorized.
The U.S. Human Rights Report for Iran for 2012 stated that: there were "3,766 flogging sentences had been implemented since 2002, 1,444 of them in 2009." See here (compiling many other sources).
Amputation sentences are often not publicly announced in Iran so statistics are harder to compile for those sentences. Given that flogging is authorized in many circumstances when amputation type sentences are not (and sometimes for reasons other than retribution) it is likely that such sentences are less common than flogging, although it isn't readily obvious if they are more, less, or equally common as death sentences. Anecdotal reporting (also here) seems to suggest that such sentences are actually significantly less common than death sentences, perhaps several to dozens of such instances in any given year. According to a 2018 Amnesty International Report:
In 2017 alone, dozens of amputation sentences were imposed and
subsequently upheld by the Supreme Court. In one case, in April 2017,
judicial authorities in Shiraz, Fars province, amputated the hand of
Hamid Moinee for robbery before executing him 10 days later for
Before carrying out the amputation sentences, the authorities often
arbitrarily imprison those convicted, even though no prison sentences
are issued against them.
According to Abdorrahman Boroumand Foundation, between 2007 and 2017,
the Iranian authorities issued at least 215 amputation sentences and
carried out 125 amputations, including at least six amputations in
See also, in accord (possibly from the same underlying source) here.
The criminal justice system in Iran publishes some statistical data, such as data on the number of people that are currently lawfully incarcerated in Iran. But since those statistics are published in Farsi, English language reports of these numbers are generally in secondary sources and it is challenging to determine whether there is enough detail to determine the number of lex talonis punishments are imposed.