The Short Answer: Not Directly
The simple answer is no, you cannot directly transfer the legal responsibility for your credit card balance to another person in the way you might transfer a car title. A credit card agreement is a deeply personal and legally binding contract between you and the card issuer. That agreement was formed based on the lender's assessment of your individual creditworthiness and ability to repay. You are solely responsible for the debt incurred on that account.
The term "balance transfer" itself refers to a specific financial product where you move a balance from one credit card to another that is also in your name. It's a tool for consolidating your own debt, often to take advantage of a lower promotional interest rate. Forcing a lender to accept a different person as the debtor would violate the original contract and introduce a level of risk they never agreed to underwrite.
However, while you can't transfer the legal obligation, there are indirect ways for another person to voluntarily take on your debt and pay it off for you. These methods effectively achieve the same goal—moving the balance off your card—but the mechanics, risks, and credit implications are very different for everyone involved. It's crucial to understand these differences to protect both your finances and your personal relationships.