Yes, you can obtain a pre-paid credit card to start establishing credit.
Answer .
There are "credit" cards available at many places where you pay in advance. Capital One is a Mastercard company...
Start with a department store card. If you can't get that start with a "secured" credit card. It will build credit and allow you to apply for a regular credit card down the road.
While a checking and savings account may factor into the decision whether or not to grant you a credit card, a much larger factor would be whether or not you have established other credit accounts.