You can consider applying for a credit card for people with limited or no credit history. You can be approved even if you do not have any credit history. Another option for you is a secured credit card. You will need to put down a minimum security deposit of around $200 to get such card. But secured cards usually have lower rates and fees, and some come without credit check. Your credit activity will be reported to the major credit bureaus, so you will be able to build your credit.