I remember reading that the US president can give an order to a civilian via some special letter. (The example given involved an IT company employee ordered to install a back-door in the company's infrastructure.) However, I cannot find this described in the Wikipedia article Powers of the president of the United States. Is my memory failing me, or is this case missing from the Wikipedia article?
The executive branch of the US government, or specific parts of it, can demand that a person do particular things, when a statute has authorized such a demand. Such demands are not usually made at the level of the President of the United States, but the president could order a specific official to take such action. For example a National Security Letter orders a person to turn over specific information, and not tell anyone about doing so, as described in this article from The New Yorker.
50 USC 3162 provides that:
(1) Any authorized investigative agency may request from any financial agency, financial institution, or holding company, or from any consumer reporting agency, such financial records, other financial information, and consumer reports as may be necessary in order to conduct any authorized law enforcement investigation, counterintelligence inquiry, or security determination. Any authorized investigative agency may also request records maintained by any commercial entity within the United States pertaining to travel by an employee in the executive branch of Government outside the United States.
(2) Requests may be made under this section where—
(i) there are reasonable grounds to believe, based on credible information, that the person is, or may be, disclosing classified information in an unauthorized manner to a foreign power or agent of a foreign power;
(ii) information the employing agency deems credible indicates the person has incurred excessive indebtedness or has acquired a level of affluence which cannot be explained by other information known to the agency; or
(iii) circumstances indicate the person had the capability and opportunity to disclose classified information which is known to have been lost or compromised to a foreign power or an agent of a foreign power.
"authorized investigative agency" is defined as:
an agency authorized by law or regulation to conduct a counterintelligence investigation or investigations of persons who are proposed for access to classified information to ascertain whether such persons satisfy the criteria for obtaining and retaining access to such information;
Accordingn to this ACLU page:
In April 2007, the ACLU filed a FOIA request seeking information about the Department of Defense and CIA's use of National Security Letters. After filing a lawsuit, the ACLU received over 500 documents from its request.
According to this ACLU page:
An ACLU lawsuit revealed that the CIA has also used National Security Letters to demand Americans' personal financial records without prior court approval. The CIA has acknowledged using National Security Letters "on a limited basis" to obtain financial information from U.S. companies.
According nto this NY Times article from Jan 13 2007:
The C.I.A. has also been issuing what are known as national security letters to gain access to financial records from American companies, though it has done so only rarely, intelligence officials say.
There are other circumstances in which an executive branch government official may order a private citizen to take specific action. Indeed, this happens in almost every case of a police arrest, except those done by an arrest warrant (which is a court order).
During the Korean War, President Truman issued an order seizing a number of steel mills, to be operated by the government, in order to stop a strike which was, he said, impeding the military effort and thus the security of the United States. This order was challenged in the case of Youngstown Sheet & Tube Co. v. Sawyer, 343 U.S. 579 (1952) and was overturned on the ground that the President was not only not-authorized by any law, but had failed to follow the provisions of a law dealing with situations of the kind at issue. In that case the Court made it clear that such a seizure would have been permitted if done in conformance with a statute, and might have been permitted had no law dealt with such cases.
Generally, in times of peace the President can not give orders to a private citizen.
However in times of war or emergencies, the courts have allowed the President to give some pretty extreme executive orders as outlined in the article you mentioned. https://en.wikipedia.org/wiki/Powers_of_the_president_of_the_United_States#Emergency_powers
Short of those extraordinary measures, there is not really a way for the President to personally order a civilian.
Keep in mind, the president is the high boss of the entire executive branch, i.e. the mechanisms of government which actually get things done.
So for instance he can command the Dept. Of Transportation or FBI or the State Department or HUD or the Federal Reserve or FEMA or dozens of other agencies. And then they have the regulatory power to act on individual citizens, to the extent they have such powers.
If he asks an agency to act genuinely beyond their purview, then they have a right to say no.
A civilian is defined as a person who is not a part of the armed forces. The Executive branch of the Federal government of the USA has hundreds of thousands of civilian employees, many in departments which have no connection with the Department of Defense or involvement with military.
As the chief executive of the USA, the president can give orders to any and all employee(s) of the executive branch of the federal government, and if those orders are legal orders and within the scope of the job the employee(s) are legally required to obey them.
So your question seems rather illogical as phased in the title.
If by civilian you mean a citizen not employed by the executive branch of the federal government of the USA, you should have said so.
The federal government does have power to give orders to private citizens. For example, employees in National parks in wilderness put up signs ordering visitors "Don't feed the bears!", and do so under orders from superiors who are ultimately subject to orders from the president.
And a number of government agencies issue various regulations for businesses, for example, to follow. The employees of those businesses who do as those regulations say are all private citizens obeying general if not specific orders from government employees ultimately under the authority of the president.