Can I apply for a bank credit card without proof of social security payment?

The proof of social security payment mentioned in your question is an auxiliary proof of your application for a bank credit card, not a necessary proof. Therefore, without this certificate, you can still apply for a bank credit card as long as you meet the credit card application conditions of the issuing bank that applies for a credit card.

Generally speaking, you need 18 years old; Having full capacity for civil conduct; Have a legal and stable job and income; Have a good credit status. You also need to provide documents to prove the above conditions, such as identity certificate, work certificate, income certificate, etc. The role of social security payment certificate is to improve the pass rate and credit limit.