Article Six, Clause 3, of the United States Constitution reads as follows:
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.
Three things are apparent from a reading of this paragraph:
1. All Senators, Representatives, and all officials of the various states have to take an oath to support the United States Constitution;
2. Unlike the oath taken by the President, the Constitution doesn't prescribe any certain language for such an oath; and
3. No religious test can be ever be required as a qualification for any office or public trust under the United States.
The oath of office that is prescribed in the U.S. Constitution for the President is found in Article III, Clause 8, and reads as follows:
Clause 8: Before he enter on the Execution of his Office, he shall take the following Oath or Affirmation:--"I do solemnly swear (or affirm) that I will faithfully execute the Office of President of the United States, and will to the best of my Ability, preserve, protect and defend the Constitution of the United States."
Note that the above oath does not require that it be made upon a Bible and does not include any reference to God, although there is nothing to prohibit a President from taking the oath on a Bible or adding the words "So help me God" to the oath.