The transient process and steady state of a current drive by means of a rotating magnetic field (RMF) are analyzed using the Lorentz transformation and linearized cold plasma wave theory. In the analysis, we consider the distortion of RMF by the screening current flowing in plasma consistently and derive the magnitude of the applied RMF which is necessary to make electrons rotate synchronously with the RMF. It is shown that the transient motion of ions plays an important role, especially in the start-up phase of the current drive, because the motion decides whether a steady state current can be driven or not. The efficiency of the current drive is shown to be equal to that of an ohmically current drive.