Can my ex-husband file fraud charges on me for a credit card that was in his name?

We were married for 13 years. We have been divorced since 2006.
He is saying that I signed for a credit card and he didn't know anything about it. He got the card so we could buy groceries...tough times. I did sign my name to the slips at the store. Now that the credit card company is coming after him (4 or so years later) he is claiming that I signed his name to get the card. And wants to file fraud charges against me. If I would have signed his name for the credit card to begin with, why would I sign my name to the slips for the purchases?? This is crazy. Is this possible?