He was elected by the "will of the people", and there isn't any "no felons" clause anywhere in the Constitution. He also hasn't been impeached, convicted, and removed for high crimes and misdemeanors. Any pardons he issues will likely be entirely legal.

(We really should require pardons to pass a bipartisan Senate committee where there is no odd-numbered tiebreaker vote and require one defection across the aisle to approve--or something like that)