You couldn't do it to control reentry, but you certainly could do it for a vertical landing system that might be a bit less technically demanding than a rocket that can descend under control with its engine running as SpaceX does.
You are limited by the mach# of the tips of the rotor, which have to be subsonic while spinning. You would want a rotor that can fold alongside the rocket and deploy and accelerate to operating RPM once it's approaching the surface, and reduce the descent rate to an acceptable level where the craft can land with its gear absorbing the landing shock in a zero forward airspeed autorotation.
This is not hard to do with a well designed gear and there are gyrocopters with gear that is designed to handle zero-forward speed autorotation landings (basically, they can cope with high descent rates by using long-stroke shock absorbers).
The rotor would simply be the simplest, lightest, cheapest system that you can come up with, that the landing gear can handle. If you could do it with two blades you'd go with that, but maybe packaging would require more blades, and you'd have to find some sweet spot with the best overall landing performance between the rotor and landing gear, and your physical packaging limitations.