A destabilizing vertical temperature gradient and a rotating magnetic field have been applied to a cylindrical column of liquid gallium. The convective flows which arise as a function of these parameters are identified. For small magnetic field strengths, a regime of stationary flow is observed. This regime is bounded by critical values of the Rayleigh and magnetic Taylor numbers. As the rotating magnetic field is increased, the critical Rayleigh number can increase by more than a factor of 10. The rotating magnetic field itself induces an instability at a critical value of the magnetic Taylor number independent of the Rayleigh number. The nature of the bifurcations (whether subcritical or supercritical) and the convective flows occurring at the critical Rayleigh numbers are dependent upon the magnetic Taylor number. For small magnetic Taylor numbers, the experimental observations are consistent with the occurrence of a single asymmetric meridional roll which is driven around the cylinder by the rotating magnetic field.