The completed Sail & Sign application form (included with your cruise documents) must be presented along with a VISA, MasterCard, Discover, or American Express. Guests may also use a Check/Debit Card, as long as it is a registered VISA or MasterCard.
Just make sure you call your credit card company before you go, and let them know that you will be using it to make purchases outside the US. They will usually ask you for the dates you'll be on the cruise. American Express is particularly apt to deny charges in foreign countries. If your credit card history shows a history of domestic purchases, and all of a sudden a charge appears from Mexico, the card can be declined, because the credit card company may assume it's a stolen card. That's why you need to notify them ahead of time.