The stability of an infinitely long magnetic fluid column of weak viscous effects is investigated. The column is subjected to a periodic azimuthal magnetic field and a rigid-body rotation. Non-axisymmetric two-dimensional perturbations are considered in this investigation. Linear analysis leads to a Mathieu equation with complex coefficients. The analytical results show that the constant magnetic field plays a stabilizing role and can be used to suppress the instability due to the rotation. When the field has been oscillating, the stabilizing role of the amplitude of the magnetic field decreases somewhat due to the applied frequency . The oscillating magnetic field plays a dual role in the stability criterion. The increase of the azimuthal wavenumber decreases the unstable region due to the increase of the column radius. A small viscosity plays a destabilizing effect due to the influence of the angular velocity in the presence of a constant or an oscillating magnetic field. A magnetic column can be stabilized at a given azimuthal wavenumber by a suitable choice of the angular velocity, the density and viscosity for the outer fluid being greater than the corresponding parameters for the inside fluid.