The stipend you receive is considered as income. So you would been approved for a student card from basically any bank.

Basically, in the US, you can get an SSN only if you have a job, anything deposited to your bank account would be considered your income.

Since the OP, already has a SSN, I assume he/she already has a job, and would have no problems getting a student card. Though as the above poster suggested, she/he would have better luck with the bank she/he already has a checking account with.