Stimulated scattering of incoherent excitons into an exciton-polariton mode leads to the buildup of a polariton condensate whose polarization is sensitive to a small seeded population that triggers the stimulated process. We show, within a semiclassical stochastic Gross-Pitaevskii model, that this mechanism enables a robust polarization memory operation: the condensate tends to align its Stokes vector with that of the seed and to maintain it for times far exceeding an individual polariton lifetime. Importantly, this single-photon-seeded regime is modeled as an initial weak excitation of the condensate mode within a semiclassical description and does not imply full quantum-state storage. We quantify the memory performance by a classical polarization-alignment metric and find that the seed polarization can remain well preserved on a nanosecond timescale under realistic parameters.