Yes, you can add your cards to the Apple Wallet application!
However, Apple Wallet currently only supports a few barcode types (QR, Aztec, PDF417 and Code 128 with iOS 9 or later). You can add all your rewards cards in Stocard with barcodes of these formats to the Apple Wallet application by clicking on the "Share Card" button at the bottom of the card display screen (below the barcode) and then selecting "Add to Apple Wallet". Since Stocard supports more barcode types than the Wallet app, there might be cards in Stocard that you cannot add to the Apple Wallet though. We apologise for the inconvenience.