This paper presents a numerical analysis of the free surface liquid metal flow driven by an alternating current magnetic field in a spinning cylindrical container. The axisymmetric flow structure is analyzed for various values of the magnetohydrodynamic interaction parameter and Ekman numbers. The governing hydrodynamic equations are solved by a spectral collocation method, and the alternating magnetic field distribution is found by a boundary-integral method. The electromagnetic and hydrodynamic fields are fully coupled via the shape of the liquid free surface. It is found that the container rotation may reduce the meridional flow significantly.