It is not possible to load a physical gift card onto your app.
You can still earn Smiles by paying with a physical gift card. In order to do so, just tap "Pay in Stores" from your app home screen and swipe to the "Scan to Earn Loyalty Only" QR code before paying. You will be able to then scan your app to earn Smiles and then pay outside the app with your gift card.
While physical gift cards aren't yet compatible with the digital platform, you may also send digital gift cards via the app by tapping into the "Gift Store" section of the app, which will allow you to send gift cards and treats from one app account to another. Redemption of those gift cards will automatically accrue Smiles, and you may track your balance right in the app!