Yes, but if you crash, you are most probably NOT covered by regular car rental insurance. Don't do it.

Goto Rent4Ring and rent a properly speced car, it has the right tires, gutted, cage, suspension, etc... and you can rent anything from a Suzuki swift to GT3. I personally only rented a Swift stage 2 or 3, which is more than enough until you learn the track... it's not fast in 0-60, but fast throttle response, coilover, and great handling. It's a lot of fun!