Field-reversed configurations (FRCs) sustained by rotating magnetic fields (RMFs) with spatial high-harmonic components have been studied in a metal flux conserver of the FRC injection experiment apparatus. In the RMF-FRC equilibrium, significant azimuthal variation of the axial magnetic field, the electron density and the electron rotation velocity are observed. This deformation of the core FRC plasma is brought about by the strong azimuthal non-uniformity of the RMF and the configuration is consistent with the continuity of the electron flow flux and the magnetic field reversal conditions. The RMF with spatial high-harmonic components provides quasi-steady current drive of high-beta and singly-connected FRC plasmas without destructive modes and will be helpful in reducing the particle loss and thermal load when applied to the fusion core plasma.