Nope. Chances are very, very low your credit card will ever be compromised with an online poker site deposit. All major poker sites use high-level encryption and standard credit card security measures to ensure all transactions are safe and secure.
AmEx also provides its cardholders with very good refund and fraud protection to safeguard the transaction. With first-rate customer support any questionable transaction will certainly be rectified quickly.
A lot of people like to auto-save their card details or keep their credit card on file for future deposits but that’s up to you to decide. It’s also up to you to keep your American Express card details private outside of any online transactions.