Upgrade iCloud storage

Yes this is possible, although you'd need to first redeem the iTunes Gift Card to the iTunes Store account that uses the same Apple ID (your iCloud address), as iTunes Store credit is an accepted form of payment for iCloud Storage. Each monthly payment will first utilize existing iTunes Store credit to cover the cost of the subscription.

From iCloud storage plans and pricing

Accepted payment methods for iCloud storage upgrades include credit cards, debit cards, and iTunes Store credit. If you don't have enough iTunes store credit to complete your upgrade, you'll be charged the remaining amount. Apple Store gift cards aren't accepted as payment for upgrading iCloud storage.