Everyone has heard the procedure to get sworn in in an American court:
Put your hand on a Holy Bible and answer yes to "Do you swear to tell the truth, the whole truth, and nothing but the truth, so help you God?"
However swearing on a Holy Bible to God has decidedly Christian roots (regardless of whether it is actually a Christian practice) in an official setting in a country with a constitution that explicitly gives freedom of religion.
As a non-Christian can you refuse to make such a vow?
In order to accommodate various objections that have arisen in recent generations, in general:
These variances are often allowed by statute.
A witnessed "solemn affirmation" has the same legal consequences as the traditional swearing on a Bible: I.e., you would be held to the same statutes and rules that apply to sworn statements.
In Torcaso v. Watkins, 367 U.S. 488 (1961), the Supreme Court held that
Neither a State nor the Federal Government can... pass laws or impose requirements which aid all religions as against nonbelievers, and neither can aid those religions based on a belief in the existence of God as against those religions founded on different beliefs.
In this case the Court struck down a statute that required state office holders to declare their belief in God as a qualification for holding any office of profit or trust in the state. In this case, Torcaso was appointed as a notary public but was refused his commission when he would not swear that he believed in God.
The Maryland Constitution at the time required a declaration of a belief in God:
[N]o religious test ought ever to be required as a qualification for any office of profit or trust in this State, other than a declaration of belief in the existence of God....
Torcaso challenged the constitutionality of the requirement. The Circuit Court rejected his argument and the Court of Appeals (the highest court in the state) held that:
The petitioner is not compelled to believe or disbelieve, under threat of punishment or other compulsion. True, unless he makes the declaration of belief, he cannot hold public office in Maryland, but he is not compelled to hold office.
So Torcaso appealed to the Supreme Court of the US and they made short work of the question and issued a unanimous opinion, concluding that:
This Maryland religious test for public office unconstitutionally invades the appellant's freedom of belief and religion, and therefore cannot be enforced against him.
There is no precise method for accommodating your preference. A person who does not want to take a religious oath pretty much just needs to ask for a secular affirmation.
