The President of the United States of America is certainly free to add "So help me God" to his oath of office, but as has been explained by Stephen Carter on the Paula Gordon Show broadcast on October 31, 2000, The Price of Power:
What about "one nation, under God" in the Pledge of Allegiance? Say it if you believe it, refrain if not, you pick, advises Mr. Carter. But it's very different and a serious problem when the Chief Justice of the United States adds '...so help me God' to the Presidential oath. That's not optional and turns the oath into a religious test, prohibited by the Constitution. George Washington said it [raySoller - of course, we don't know that], but the phrase should not be there.
Stephen Carter Professor of Law, Yale University, and an author. A former clerk to Supreme Court Justice Thurgood Marshall, Mr. Carter is among the nation's leading experts on constitutional law. Mr. Carter confronts what he views as challenges to America's democracy in his several books, including The Culture of Disbelief, Civility, Integrity and God's Name in Vain.