You can use any kind of drill for this process. Find a drill bit that has just enough diameter to drill out the center of the screw head. If it's a Phillips head screw, find a bit that just covers the star shape in the center.
Slowly begin drilling the center out of the screw head. It should go pretty fast. If the screw was soft enough to strip it should be nothing for a steel drill bit. You don't need to drill too deep, just far enough to disconnect the screw head from the rest of it. Usually it will start to spin as it separates.