It has been proposed that stored proton or heavy ion beams can be polarized by spatially separating particles with opposite spin directions, using the Stern-Gerlach effect in alternating quadrupole fields. The growth rate of the vertival betatron amplitude is calculated for beam halves with opposite polarizations rotating in the horizontal plane, at intrinsic spin resonance a γ ± νy = integer. This polarization method would work best with rings having large diameter, low vertical emittance, low vertical betatron tune, and strong superconducting quadrupoles. Provided that suitable strong quadrupoles exist, the method might advantageously replace the present technique for obtaining polarized proton or heavy ion beams, where low energy polarized beams are first generated by a source and then accelerated through numerous depolarizing resonances up to the final energy. Although the proposed self-polarization in the present colliders and storage rings might be impractically slow, it is shown that in a purpose-built machine the vertical splitting rate of the beam might be reasonably fast compared with the beam blowup or decay.