Don't have a track car, no problem....
 

I'll bet those are equipped with GPS. They know where the car is at all times and how fast it's going. You sure you want to rent it?

I would read the rental aggreement carefully. If it is the standard agreement, and says nothing about race tracks, I would be tempted to go play.

After the lessons learned back in the 60's, there is most likely some disclaimers in bold print in the agreement.

Don't forget to get the optional "Collision Damage" insurance.