Building credit without a Social Security number can be quite difficult, but it isn't impossible. Credit card issuers can't require you to provide a Social Security number.
Instead, many credit card issuers ask for an individual taxpayer identification number (ITIN). An ITIN is a nine-digit identifier that acts like a Social Security number. For information on how to apply for an ITIN, visit General ITIN information on the IRS website.
The tricky thing is that not all credit card companies allow the use of an ITIN to apply for a credit card. This means you will need to do some research to learn which companies allow you to use your ITIN. One credit card company that accepts ITINs during the application is Yendo. Yendo also does not perform a credit check.
Credit card issuers that accept ITIN numbers may deny your application if you don't have a credit history. So, go ahead and apply for a regular credit card with your ITIN even if you lack a credit history. But if you are denied, you should next apply for a secured credit card to establish that history.
Qualifying for a secured credit card is easier than for a regular card because you put down a deposit as collateral. This reduces risk for the card company because it can collect money from your initial deposit if you don't pay your balance on time. The credit limit on secured cards usually equals the amount of your deposit.
To keep your secured card (and credit!) in good standing, always pay your balance off on time and in full. Once you have a good payment record on your secured credit card, you may qualify for a regular, unsecured credit card.