It looks to be a 5/16" or 3/8" bolt. Also, It was obviously a sign that you needed new tires. If you had new tires, the screw would have only punctured a little. I just recently had an 1.5" screw go in my tire, but since they were nearly new, it only put a small hole. When i pulled the nail out, the rubber immediately resealed itself and didnt leak, but i plugged anyway to prevent something happening later on.

just get a new tire and you'll be fine/better than you were before.