How can I add Apple Card as a payment method on my iPad?

There is no Wallet App for iPad.

You should however be able to add your Apple Card to the Wallet & Apple Pay option in the Settings app as long as the iPad is logged in with the same Apple ID as the iPhone used to request the Apple Card.

click here ➜ How to add Apple Card to your Apple devices - Apple Support

There is a card section in Settings app on iPad. But iPads lack NFC and really aren’t designed for Apple Pay (Tap-To-Pay) transactions. However, you can do manual entry online transactions on some websites.