How do I add a gift card to my Apple wallet

Presuming it is an Apple Gift Card, you don't add the card to the Apple Wallet, you have to redeem it to your Apple ID Balance as outlined in How to redeem your Apple Gift Card or App Store & iTunes gift card.

Marshimallo wrote:

No, it is a restaurant gift card

In that case, I don't think that is possible, but you can consult If you can't add a card to Apple Wallet to use with Apple Pay which states:

"If you see the message "Could Not Add Card" or "Invalid Card," contact your bank or card issuer.

Apple does not approve or decline cards for use with Apple Pay. If your card was declined, contact your bank or card issuer.

If you need help adding a card, learn how to set up Apple Pay."