It's not a requirement. It's just ceremonial. They could put their hand on top of Mein Kampf if they wanted to.
(quick from AI) George Washington: Started the tradition of using a Bible for the presidential oath. Theodore Roosevelt: Took the oath of office without a Bible after William McKinley's assassination. John Quincy Adams: Placed his hand on a law book during his inauguration. Lyndon B. Johnson: Took the oath on a Catholic missal following John F. Kennedy's assassination.