Magnetic vortex dynamics mediated by spin-polarized ac current of different amplitudes and frequencies are investigated by micromagnetic simulations in a system lacking structure inversion symmetry. Micromagnetic calculations reveal that the critical current density required to induce vortex core reversal may be decreased to below 1010 A m−2 due to strong transverse magnetic field by Rashba effect. We also find the spin torque of ac current plays a trivial role in magnetic vortex dynamics in a broken inversion symmetry system when the current density is on the order of 1010 A m−2 and the current with frequency close to the vortex eigenfrequency is the most efficient for reversal.