We propose theoretically a spin memory effect in quantum dots and single molecules with strong electron-vibron interaction and coupled to ferromagnetic leads. The controlled electrical switching between spin states is achieved due to an interplay between Franck-Condon blockade of electron transport at low voltages and spin-dependent tunneling at high voltages. Spin lifetimes, currents, and spin polarizations are calculated as a function of the bias voltage by the master-equation method. We further propose to use a third ferromagnetic tunneling contact to probe and readout the spin state.