Controllable propulsion of microscale and nanoscale devices enhanced with additional functionality would enable the realization of miniaturized robotic swimmers applicable to transport and assembly, actuators, and drug delivery systems. Following biological examples, existing magnetically actuated microswimmers have been designed to use flexibility or chirality, presenting fabrication challenges. Here we show that, contrary to biomimetic expectations, magnetically actuated geometries with neither flexibility nor chirality can produce propulsion, through both experimental demonstration and a theoretical analysis, which elucidates the fundamental constraints on micropropulsion via magnetetic rotation. Our results advance existing paradigms of low-Reynolds-number propulsion, possibly enabling simpler fabrication and design of microswimmers and nanoswimmers.