Credit card applications require a Social Security Number as a form of identification, notes NerdWallet. As of 2015, those who don't have a SSN do not have to provide one on credit card applications. In such cases, obtaining an Individual Taxpayer Identification Number can serve as a substitute.
Not all financial institutions that handle credit card applications accept Individual Taxpayer Identification Numbers from the Internal Revenue Service, according to NerdWallet. No matter if a person is an immigrant of the U.S. or a natural-born citizen, he is still eligible to receive an identification number. Even without a SSN, a person can be added as an authorized user on a credit card account, notes Bankrate.