The best answer for this is to open a Checking Account first.

When you apply for a credit card they will ask you if you have a Checking Account & Savings Account? Heavily relying on the fact that you are responsible enough to have your own checking account.

They also will like the fact that you have a checking account so that they can maybe ask you to open one up with them, since you are now a cardholder.

However, all in all always have a Checking Account open before you attempt to apply for a credit card.

Banks will also see when you apply that you don’t have a checking account and in complete honesty, that doesn’t make you look very responsible. They would expect this from an 18 or 19 year old (not to have a checking account open) however, if you are in your 20’s 30’s and up and you don’t have a checking account, if I would want to know why? Don’t you think the banks would be more curious.

There should be nothing stopping you from having a checking account. Checking accounts are relied upon to pay your bills. So, if you are going to apply for a credit card don’t you think that the bank would like you to have a checking account? So that they know that you have some type of means to pay your bills?