He can't be court martialed, and he can't be convicted of treason either. He isn't a member of the military and Russia is not officially an enemy of America. To put it into perspective, even in the Cold War, when the Rosenbergs were convicted of espionage for giving the Soviet Union information on radar, sonar, jet propulsion, and nuclear secrets, they still weren't convicted of treason, because technically the USSR was not an enemy of America, which historically has been interpreted as "Congress has actually declared war on them" something we haven't done since WW2. If you were to look up a list of people convicted of treason in America you will note it largely stops after 1945.

And that is a very good thing, especially from the perspective that many nations still consider mild criticism of the head of state treason.

He can, however, suddenly be subjected to much, much more scrutiny than even an actually innocent person would be comfortable with for interfering with American... "Interests."