Yes, one can refuse to swear on the Bible in a U.S. Court because the Constitution's First Amendment prohibits the government from coercing a person into a religious act, which includes taking a religious oath. Further, this act of 'swearing on the Bible' is truly an unholy and devilish act, as per Matthew 5:34-37: "But I tell you, do not swear an oath at all: either by heaven, for it is God’s throne; or by the earth, for it is his footstool; or by Jerusalem, for it is the city of the Great King. And do not swear by your head, for you cannot make even one hair white or black. All you need to say is simply ‘Yes’ or ‘No’; anything beyond this comes from the evil one." Therefore, no true Christian should ever swear upon the Bible, nor swear an oath regarding anything at all for that matter!