What could be more iconic than the image of someone with their hand on the Bible, swearing an oath. The question before us is "Must an oath be taken on a religious object?"
The answer, as we might guess, is "no." BUT!! There's more to it. While other objects can be used (Teddy Roosevelt took his Oath of Office on law books), one can swear without any object at all. Nope. You don't need a book, a copy of the Constitution, a City Charter, or anything at all.
In fact, you don't even need to take the Oath of Office to become president. It is not mandated in the Constitution. How about that? If you're elected to a local office, it might be different though.
How about our bidding? Do we swear to tell the truth?