You can check if you have are pre-qualified for a credit card before you actually apply. Accepting the offer may or may not result in an inquiry on your credit report(s). But, at least you have an idea if you have a good chance of being approved.
American Express
Bank of America
Barclaycard
Barclaycard Ring
Capital One
Chase
Citibank
Credit One Bank
Discover
Merrick Bank
US Bank