I’m having trouble setting up an iTunes account with an iTunes gift card

It may have to be done in a specific manner:

Create or use your Apple ID without a payment method - https://support.apple.com/HT204034 - "When you use your Apple ID to sign in to the iTunes Store, App Store, or iBooks Store for the first time, you're asked to enter a payment method so that you can purchase items from the store. Follow these steps if you don't want to associate a payment method with your account." - more information: https://discussions.apple.com/message/33067311#message33067311