Before you apply for a credit card, make sure you have a U.S. Social Security number. You will need it to fill out an application form.
A credit card for people with no credit history is a good option for you. Some of the cards have rewards programs and others have 0% introductory APR periods. So compare the cards to find the best one for you.
You can also consider applying for a secured credit card. They do not have rewards programs, but come with lower APRs. You will need to put down a security deposit before you can get a secured card.