Simply ask them…
Interest rates are based on your credit worthiness. If you are carrying balances on your credit card, and especially if your paying the minimum or just slightly above – it’s very unlikely that the credit card company will agree to lower your rate.
I would suggest increasing your payments in order to lower the balance you’re carrying, and even better – paying it in full if you can.
When you pay your balance in full every month – you won’t be charged interest at all. Not only you’re saving money, the credit card company is very likely to lower your APR.
After a few month of zero balance – simply call the customer support number and ask them. The worst they can do is say no.
Good luck!