How to add apple gift card to wallet?

Use Wallet on your iPhone or iPod touch - Apple Support doesn't mention anything about adding "Gift Cards."

"With Wallet, you can keep your credit, debit, and prepaid cards, store cards, boarding passes, movie tickets, coupons, rewards cards, student ID cards, and more in one place."

What "Gift Card" are you trying to add?

You should consider redeeming the Gift Card to one of your other existing payment methods.

Apple gift card

You cannot add an Apple or iTunes gift card to wallet. You redeem those cards in the App Store or iTunes.

I happen to have 3 app / iTunes gift cards IN my wallet, I'm try to redeem them.