Absolutely, and it doesn't even have to be a Disney-specific credit card (though, there are Disney World credit cards, too). For instance, using a cash-back rewards card for your everyday purchases and committing to putting those rewards into a savings account specifically for your next vacation – Disney or otherwise – is one way to use your rewards to help pay for your vacation.
Another way to vacation with Disney using credit card rewards is to make good use of your cards' travel redemption options. Some cards, for example, allow you to redeem your rewards for statement credit to cover travel related purchases made on your card. Consequently, you could pay for everything from your flights to your theme park tickets to hotel stays to transportation to and from the airport with travel rewards. Other cards allow you to transfer rewards to hotel and airline loyalty programs, which could mean even more value for you as your plan your trip.
The bottom line is that credit card rewards are an excellent opportunity to offset some of the cost of a pricey adventure to the Happiest Place on Earth.