Yes, but you'll need a little help. When lawmakers wrote the Credit CARD Act in response to the 2008 financial crisis, they pushed through changes designed to protect young Americans from making mistakes with money. Under federal banking regulations, banks can only accept credit card applications from Americans below the age of 21 in a handful of circumstances:
Don't co-sign for a credit card offer unless you've worked out a clear financial strategy with your parents. For instance, Discover Card and Capital One offer some of today's best student credit cards. They replace the needs for parents to wire cash to your campus, but they also show your parents exactly how you're spending that money.
Student credit cards also carry some risk. Miss a payment or exceed your balance, and your co-signer's credit score can suffer. Likewise, if your co-signer uses the account and can't pay their share of the bill, you're on the hook for finance charges and penalties at a time in your life when you don't want black marks on your credit report.
According to University of Houston Law Center Professor Jim Hawkins, credit card companies don't have to check your reported income against your tax return or your pay stubs. Professor Hawkins discovered that some applicants report their student loans as income, triggering an exception in the rules. Therefore, it's not impossible for you to get a student credit card on your own.
At your age, I'd really recommend signing up for a free prepaid debit card from American Express. You and your parents can fund your card for free via direct deposit or bank transfer, and some versions of their cards offer free reloads at participating retail stores. Learn how to manage virtual money with a debit card now, so you'll avoid credit card problems after you leave school.