I've used a Disney Visa Rewards Card to pay a portion of my dues for the past few years. As Michael posted, you have to call Member Administration to do so.
Basically, you first must transfer your rewards to a rewards card. (You'll have to order a card if you do not have one or if your existing card has expired). You can do the transfer online at the Disney Visa website. Once the rewards are transferred to the card, you can call MA. The CM will ask for the number of the card. Then you can pay the balance with another credit card.