That's never been litigated, so the answer is "not known."
The Department of Justice's Office of Legal Counsel has issued several opinions over the years saying no, they do not believe the President can pardon himself.
Quote:
Pursuant to Article II, Section 2 of the Constitution, the "Power to grant Reprieves and Pardons for Offenses against the United States, except in Cases of Impeachment," is vested in the President. This raises the question whether the President can pardon himself. Under the fundamental rule that no one may be a judge in his own case, it would seem that the question should be answered in the negative.
https://www.justice.gov/file/147746/dl?inlineThat's just an "opinion" by an office and not a Court, but that's the existing "on the books" view of it by the Executive Branch.
(*** For those who aren't familiar, OLC is essentially the Executive Branch and President's general counsel and they write various legal memos on different issues. They also are the ones who typically review Executive Orders and other executive actions.)
