Indeed he can, but he'd be wise to also remember this part of the Constitution (From Art. VI).
The Senators and Representatives before mentioned, and the Members of the several State Legislatures, and all executive and judicial Officers, both of the United States and of the several States, shall be bound by Oath or Affirmation, to support this Constitution; but no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States.
Sheesh. There is no religious test here. Get real.
A religious test would be making one of the legal qualifications for public office membership in a particular church or sect. This is nothing of the sort.