We present a theory for spin-polarized transport through a generic organic polymer connected to ferromagnetic leads with arbitrary angle theta between their magnetization directions, taking into account the polaron and bipolaron states as effective charge and spin carriers. Within a diffusive description of polaron-bipolaron transport including polaron-bipolaron conversion, we find that the bipolaron density depends on the angle theta. This is remarkable, given the fact that bipolarons are spinless quasiparticles, and opens a new way to probe spin accumulation in organic polymers.