Yes. You can use the value of the gift card as your cost basis. The basis of a gift is the donor's adjusted basis or fair market value at the time the gift was made.
Since the donor’s cost is presumably the face value of the gift card and it has the fair market value listed on the card that would be your cost basis.
There are a few adjustments that should not apply to a $20 gift card.
Learn more at What is the basis of property received as a gift?
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