The Presidential oath of office is described in Article II, section 1 of the Constitution:
Nothing in this section requires that the oath of office be taken on the Bible. Neither do the words "so help me God" appear in the oath. While Presidents often include this phrase in their inauguration ceremonies, the words are customary; they are not required by the Constitution and have no legal significance.
Additionally, we note that the words required by the Constitution are described as an "Oath or Affirmation," and that the President is allowed to simply affirm his faithfulness to the Constitution. The word "affirmation" was inserted in this section precisely to allow Presidents to avoid swearing oaths to God as a condition of taking office. This provision seems particularly intended for Quakers (who had religious objections to taking oaths), but it is worded broadly enough to encompass any person who objects to taking an oath, including non-theists.
At the time of the Constitution several states allowed Quakers to escape taking an oath as a condition of assuming elected office. The 1780 Constitution of the state of Massachusetts, for example, provided that:
Conversely, the 1776 Delaware and 1777 Vermont constitutions did not restrict affirmations to Quakers. Like the Federal Constitution, these states allowed any citizen otherwise qualified for public office to affirm loyalty to a state, if conscientiously scrupulous of taking an oath. Still, the federal Constitution went far beyond the practices of even these states by prohibiting religious tests for public office (see below).
Finally, we note that even the "oath" form of the words prescribed by Article II, section 1 is secular in content. Unlike the oaths required in some states, the federal Constitution does not specify to whom the President "swears." God is not mentioned; it is almost as if the framers purposely worded the oath to allow the President decide for himself who, if anything, is being sworn to.
Oathtaking is not rocket science. If the framers wanted Presidents to invoke God when taking the oath of office they could have worded the oath to accomplish that objective. Instead, the constitutional oath of office contains no reference to God, need not be administered on the Bible, and need not even be considered an oath. Contrary to the accommodationist argument, Article II, section 1 is evidence that the framers intended the federal government to be secular in its operation.
Oaths of office for other federal and state officials are described in Article VI of the Constitution:
Joseph Story, an early Justice of the Supreme Court and the author of the first detailed commentary on the United States Constitution, comments on the oath or affirmation clause of the Constitution as follows:
In other words, the Constitution guarantees all federal and state officials the right to avoid taking oaths of office. Further, the Constitution guarantees that there will be no religious tests for federal office. In the words of Joseph Story, the effect of these provisions is to "cut off for ever every pretense of any alliance between church and state in the national government." Additionally, these clauses moved the Constitution well beyond contemporary state constitutions in terms of their provisions for religious freedom.
Presidents and other federal officials may swear on the Bible and say the words "so help me God," but this does not make the Constitution any less secular. The Constitution requires nothing of federal officers in the way of religion. The framers saw no need to refer to God in the oath of office, and explicitly provided an alternative to the oath that guaranteed secularity.