A rotating vortex-antivortex dipole may be generated due to spin-polarized current flowing through a nano-aperture in a magnetic element. The vortex dipole dynamics is analyzed using the Landau-Lifshitz equation including a Slonczewski spin-torque term for in-plane spin-current polarization. The spin-torque acts to stabilize the vortex dipole at a definite vortex-antivortex separation. We establish that the vortex dipole is set in steady state rotational motion. An external in-plane magnetic field can be used to tune the frequency of rotation. We derive analytically a relation for the frequency of rotation and we find numerically steady-state rotating vortex-antivortex pairs in a more realistic model. The rotating pair under a spin-polarized current is an attractor of the motion, therefore it is expected to be a stable state.