We propose, theoretically, a type of quantum field effect transistor that operates purely on the flow of spin current in the absence of charge current. This spin field effect transistor (SFET) is constructed without magnetic material, but with the help of a spin flip mechanism provided by a rotating external magnetic field. The SFET generates a constant instantaneous spin current that is sensitively controllable by a gate voltage as well as by the frequency and strength of the rotating field. The characteristics of a carbon nanotube based SFET is provided as an example.