Answer:
If you have a 611 credit score, there's a good chance you will not be approved when applying for a credit card, assuming it requires good or excellent credit.
Put simply, most creditors refer to credit scores below 620 as "subprime." So a credit score below that range likely won't be sufficient for most credit card approvals.
If you apply and aren't approved, you may want to inquire about getting a so-called "bad credit" credit card. Alternatively, you can visit your local bank or credit union and ask about available options.
If that too is out of the question, you may have to settle for a secured credit card, which requires cash as collateral.
Just keep in mind that credit scoring is very subjective, and credit card issuers look beyond your actual three-digit score to determine your creditworthiness.