Yes, he can, from Andrew Napolitano at lewrockwell.com:
Most presidential pardons — indeed all pardons that President Donald Trump has issued — have been for specific crimes of which the subject of the pardon has already been charged and convicted. Yet, Trump, never one to be restrained by precedent, has let it be hinted that he might issue prophylactic pardons to relatives and colleagues who have neither been convicted nor charged with any crimes. And he might pardon himself. Can he do that?
The short answer is yes. Here is the backstory.
The pardoning power is expressly and exclusively granted to the president in the Constitution. Article Two, Section 2, Clause 1, states that the president “shall have Power to grant Reprieves and Pardons for Offenses against the United States, except in cases of impeachment.” When unpacked, that broad language reveals that the president can only pardon for federal crimes, not for anyone’s impeachment, and he does not need the approval of anyone else in the government.
Trump is the subject of a criminal investigation in New York City for alleged or potential violations of state laws. But the existence of a state criminal probe of the president does not impair his ability to insulate himself from the legal consequences of a federal criminal probe, since it is clear that the president cannot pardon anyone — including himself — for state offenses.