Renegotiate if needed
If you are unable to convince your credit card provider to reduce your interest rate, ask them what you can do to qualify for a lower rate in the future. If you have a history of making late payments, start making your credit card payments on time.
Try to pay off some of the debts you have, other than your credit card, to increase your debt-to-income ratio. Once you have a reasonably decent credit score, try to negotiate with your credit card company again.