A bluesy raspyness isn't something I would try doing intentionally, you'll most likely end up hurting your throat / voice. It's better to make do with what you've got though rather than try and sound like someone else.
Just sing and sing and sing. Sing everything as much as you can. Spend the next 5 years singing every song you know and learn the words to every new song you hear. In time, as you become a better singer, you'll learn to control your voice and be able to do things you hadn't been able to do in the past.