We report on noise-induced spin ordering in a collective quasiparticle system: spinor stochastic resonance. Synergetic interplay of a polarization-modulated signal and a polarization noise allows us to switch coherently between the two metastable states of a microcavity-polariton spin bistable system. Spinor stochastic resonance is demonstrated in a zero-dimensional GaAs based microcavity. The resonance behaviors of both the spin amplification and the signal-to-noise ratio are experimentally evidenced as a function of the noise strength for different amplitude modulations. They are theoretically reproduced using a spinor Gross-Pitaevskii equation driven by a randomly polarized laser field.