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If you have Social Security number (SSN) you can get a credit card. In addition you will need to provide your permanent address. If you have a job or some other kind of income and a checking or savings account, that will increase your chances to get a card. Since you are a student, consider applying for a student credit card.
As for APR, it is an annual percentage rate you will pay on any outstanding balances. If you pay the balance on your credit card in full every month and do not max out your credit card you won’t be charged any interest. If you do not pay off the balance in full every month and make only minimum due payments, the interest will accrue. So pay off the amount you owe if you do not want to pay the interest.