As with most types of loans, you can sign up for a credit card with a co-borrower. This approach is commonly used by spouses to acquire joint credit accounts. Additionally, federal law requires credit card applicants under the age of 21 to have a co-signer, such as a parent, if they don't have proof of income.
Lenders need to feel comfortable in your ability to repay debt before issuing you a credit card. So, if you ask someone to be your co-borrower because of poor or no credit history, it's necessary that that person have a good to excellent credit rating. Another advantage of having a responsible co-borrower is that you both benefit from enhanced credit ratings if the card is managed responsibly, including keeping low debt balances and making on-time payments.