  We develop a theory of spin fluctuations of exciton-polaritons in a
semiconductor microcavity under the non-resonant unpolarized pumping. It is
shown that the corresponding spin noise is sensitive to the scattering rates in
the system, occupation of the ground state, statistics of polaritons, and
interactions. The spin noise spectrum drastically narrows in the polariton
lasing regime due to formation of a polariton condensate, while its shape can
become non-Lorentzian owing to interaction-induced spin decoherence.
