Yes, there are definitely classes for people your age. And it is fun!! You might have to shop around to find a program that's right for you, though -- some studios really only focus on adults. Others have a variety of programs for all ages, and still others have special programs for young people that are quite popular.
A lot depends on where you are. If you're living in the New York City area or in New Jersey, you can definitely find a young dancers program. There's also some programs in Los Angeles and San Francisco. I can't speak for the rest of the country, but you can definitely check around.