Yes! Just log in to your account and visit the "Autoship" section of your account. Then on the bottom of the autoship screen, click on the "Edit Payment Method / Billing Address" button.
To add a new credit/debit card: In the dropdown on the top of the popup, click on "Use new card...". Fill in the form with your new payment information and hit save. The next time your subscription renews, it will use this card.
To update your billing address: Leave the dropdown as is and modify the address in the form below, then hit save.