Actuator materials producing rotation are rare and demonstrated rotations are small, though rotary systems like electric motors, pumps, turbines and compressors are widely needed and utilized. Present motors can be rather complex and, therefore, difficult to miniaturize. We show that a short electrolyte-filled twist spun carbon nanotube yarn, which is much thinner than a human hair, functions as a torsional artificial muscle in a simple three-electrode electrochemical system, providing a reversible 15,000° rotation and 590 revolutions/minute. A hydrostatic actuation mechanism, like for nature’s muscular hydrostats, explains the simultaneous occurrence of lengthwise contraction and torsional rotation during the yarn volume increase caused by electrochemical double-layer charge injection. Use of a torsional yarn muscle as a mixer for a fluidic chip is demonstrated.