Does the Mazda miata have a rotary engine?

There isn't a commercially available Mazda Miata with a rotary engine; what You'll be able to buy is going to be a normal piston-driven inline 4Cylinder. Now, there was a Mazda prototype racing car, the 787B, which had Mazda's WankELRotary engine. This RX-8 powered vehicle isn't for the casual buyer, given the high and constant cost of maintaining it. In short, unless You're driving a Mazda with an RX label, You're on pistons.