You can get an Apple Card without SSN, by using your ITIN (Individual Taxpayer Identification Number) instead. You can just fill in this information in the box where you would normally put your SSN.
Please note that the only way to apply for the Apple Card is through either the card's webpage or the Wallet app on an iOS device, such as an iPhone or iPad.
How to Get an Apple Card Without SSN
Sign in to iCloud and open the Wallet app on your device.
Tap the “Add” button (a plus sign), select the Apple Card, and click “continue.”
Fill in the application with your name, date of birth, phone number, address, last four ITIN digits, citizenship status, and income.
Accept the terms and conditions and submit your application.
If you are approved for the Apple Card, you will see an initial credit limit and APR. You can choose whether to accept or reject the offer. If you accept, there will be a hard pull of your credit. Otherwise, there will not be a hard pull, but you will not get the card.