Can I apply for a credit card without a social security card?

Of course you can apply. Whether there is social security or not has little effect on applying for a credit card. I suggest that you provide proof of identity, monthly bank consumption and financial ability: it can be bank payroll records, income tax withholding certificates, or market value certificates of your house, car, deposit and investment (such as a copy of real estate license/car driving license/bank time deposit certificate) and other materials that can prove your financial ability. Other documents for reference include: personal account list of social insurance in the last 6 months, water, electricity and gas bills, credit card bills of other banks, etc. You can try to apply, which can effectively improve the success rate of application.

Because each bank's application standard is different, you can call the bank's customer service phone or visit the bank in official website to find out. Have a good time applying for the card.