The sustainment of a field-reversed configuration by means of a rotating magnetic field (RMF) is studied by the numerical simulation. It has been shown that the RMF applied externally on an FRC immediately after the production by a field-reversed theta pinch is penetrated into the plasma to drive a steady current, before the FRC fades out. There is a threshold value of the RMF which can maintain the FRC by the method. Since the RMF used in the present study is fairly large, we should optimize the parameters of the RMF to reduce the magnitude of the RMF required for sustaining the FRC. The method of applying the RMF to the FRC, however, may be effective for sustaining the hot and dense FRC in a steady state.