A spin-polarized current with the polarization direction perpendicular to a disk in the vortex ground state will result in renormalization of the effective damping of excitations on this state. As the current is increased to a threshold current Ic the effective damping will be zero and the lowest threshold current corresponds to the vortex gyrotropic mode. For larger values of the current the excitation is a nonlinear gyrotropic mode having nonsmall amplitudes and larger frequency than the linear mode. This effect occurs for any mode of the vortex-state disk, and the value of Ic is proportional to the mode frequency.