If the gift card is something that you actually purchased and gave away to a customer, then you can deduct it as a business expense. For example, if you purchased a gift card for Amazon and gave it away to a customer, then you can deduct the cost of the gift card you purchased.
If you were giving away a gift card or gift certificate for your own business, then you cannot deduct the cost or face value of the gift card. The only expense you can deduct would be the actual cost of the card or certificate if you had to pay for it to be printed or created.
When a customer redeemed the gift card or gift certificate, it will reduce your income because the patron using the certificate will not pay you, but they will receive goods or services in exchange for the certificate. You will still incur expenses for those goods or services.