No. He didn’t have his hand in the Bible.
But I think it’s because he was already sworn in and because his faith nor conviction to stay within his faith are defined by where he places his hand.
Beyond that - What song played as soon as he was done with the Oath?
“His Truth Is Marching On” - That song is about Jesus Christ.
He then said “We will not forget God in America”.
He has made it pretty apparent where his faith lies.
Mike