In this video Peterson says that
... anybody into the Armed Forces if they have an IQ of less than 83...
Is this true? What law is this supposed restriction based on?
Applicants are required by military regulation to have a percentile score on a standardized test called the ASVAB that is 31 or more, which is roughly comparable to an IQ score on the Stanford-Binet scale of a little bit less than 92, for high school graduates seeking to enter the Army or Navy (other services have more strict requirements and applicants with only a GED or to the national guard must have an ASVAB score in the 50th percentile which is equivalent to an IQ of 100).
But, U.S. law allows the Department of Defense to allow people with a percentile score on the ASVAB that is as low as 10 if it chooses to do so. An IQ score of 83 on the Stanford-Binet scale is the 14th percentile of the general population and is fairly close to a 10th percentile score on the ASVAB, although the conversion is not very exact, because ASVAB test takers have fewer people in the top and the bottom of the IQ range than the general population.
So, the assertion that the law prohibits people with an IQ score of 83 or less from serving in the U.S. military is close to the truth, although the reality is somewhat more complicated.
The U.S. military sets, as a matter of policy in a government regulation at the Department of Defense level, certain minimum requirements for people who seek to enter military services. Some of the main requirements are found here. There are also requirements not described there such as a requirement that people enlisting may not have juvenile or criminal records of a certain severity.
Additional requirements apply to certain military occupational specialties within the military. For example, someone may qualify to be an Army cook, but not to be a military intelligence specialist in the Air Force.
If a person does not meet those requirements, that person is not allowed to serve unless a waiver is obtained from a person with the authority to do so, and even the kind of exceptions that can be made and the factors that must be considered when making an exception on a case by case basis, are specified by a regulation or official pronouncement of the Department of Defense.
Among the requirements specified by regulation are educational requirements (a high school diploma or GED subject to some exceptions). Applicants are also required to take the Armed Services Vocational Aptitude Battery (ASVAB) from which the applicant receives an AFQT score is equal to the applicant's percentile ranking of the applicant's raw score on the test. An applicant's AFQT score is strongly correlated with a applicant's IQ score on a traditional IQ test.
Applicants with a GED rather than a high school diploma, and all national guard applicants, must score at least 50. Applicants with high school diplomas must score at least 31 to enter the Army or the Navy, 32 to enter the Marines, and 36 to enter the Air Force or the Coast Guard, as a matter of federal regulation.
ASVAB scores from one year are not necessarily full comparable to ASVAB scores from another year because the test is rescaled from time to time based, among other things, on the scores earned by people who take the test.
For all practical purposes, a Department of Defense regulation has the force of law with respect to an individual applicant seeking to enlist in the military, or an individual recruiter evaluating military applicants.
But, Congress has vested the task of setting exact cutoffs and deciding which tests to use to evaluate applicants in the U.S. military and it changes its regulations from time to time based upon the recruiting targets that it needs to meet to satisfy Congressionally set force sizes, and the quality of the applicant pool, subject to the requirement that no one with an AFQT score of below 31 may enlist without a high school diploma, that everyone that enlists must have an AFQT score of at least 10, pursuant to 10 USC 520, AND that no more than 20% of enlisted soldiers may have an AFQT score below 31.
AFQT score percentiles on the AVSAB and IQ percentiles aren't completely comparable to each other, however, because IQ percentiles are based on the general population and AFQT scores are based upon people who take the test. People with very high IQs (who tend to go to college rather than the military in the U.S.) and people with very low IQs (who tend to not even try to enlist in the military, knowing that it is futile) are underrepresented among AVSAB test takers, so very low AFQT scores correspond to somewhat higher IQ percentiles, while very high AFQT scores correspond to somewhat lower IQ percentiles.
IQ scores are scaled with a Standard Deviation of either 15 (Weschler) or 16 (Stanford-Binet), and a mean of 100 for the general population. In a 16 point standard deviation IQ test, the 30th percentile is an IQ score of 92 and an IQ score of 83 is the 14th percentile.
It isn't unreasonable to estimate that an AFQT score of 10 corresponds to an IQ score of 83, although I haven't seen any source making that exact conversion. My best guess is that the minimum AFQT score of 10 corresponds to an IQ score of more than 83 but less than 92 on a Stanford-Binet scale.
For comparison's sake, an IQ score of 70 is normally considered developmentally disabled (a.k.a. mentally retarded).
The minimum IQ score for entry into the military according to Congress would be considered a bit "dull", but within the range of ordinary self-sufficient people in the general population.
The minimum IQ score for entry into the military by current regulations of about 92 would be within the "normal" range of 90-110 that includes about half of the general population.
UPDATE (September 26, 2019): While this is a law that the U.S. military is duty bound to honor, it isn't at all obvious that anyone, with the possible exception of Congress or at least a majority of one house of Congress, would have standing to bring a civil action in court to enforce this requirement. To have standing one would have to show an actual injury from the violation to you personally, and that in turn, would be extremely hard to show in a casual manner. Generally speaking, however, mere statistical evidence of some actual injury to you on average is insufficient. One could imagine a case where a low IQ person's mistake harmed a fellow soldier, but it would be almost impossible in practice to segregate the IQ contribution to the mistake happening to myriad other facts that could also have led to the mistake (e.g. insufficient training).
It is not true for a few reasons. First, the number is 81, sort of. 10 USC 520 specifies a minimum 31st percentile on the Armed Forces Qualification Test; see this Q&A for an analysis of the relationship between IQ and AFQT. The law is not stated in terms of IQ, it's based on a different test. However, this addresses enlistment, not civilian employment by the armed forces. There is no law prohibiting civilian employment of people who don't test well; the relevant question would be whether the individual has useful skills.