There’s no law requiring you to swear on a Bible, or on any religious text at all. You can simply raise your hand and take an oath or make an affirmation. The Constitution prohibits religious tests for public office and protects freedom of religion, so there is no legal requirement to use any particular book.

More importantly, the law doesn’t care what object you swore on. What matters is that you made a legally binding oath or affirmation. If you knowingly lie after taking that oath in a legal proceeding, you’ve committed perjury. The book itself has no legal significance.