The effect of a rotating magnetic field (RMF) on the stability of a fluid contained in a cylindrical column and heated from below is investigated. The RMF increases the critical Rayleigh number for asymmetric flow modes but does not affect the onset of instability for axisymmetric modes. The critical Rayleigh number is dependent upon the relative penetration of the magnetic field into the cylinder and the Prandtl number of the fluid. Instability first develops in the form of a single asymmetric meridional roll rotating around the axis of the cylinder, driven by the azimuthal component of the magnetic field.