  We show how anisotropy in momentum of the gluon distribution in
ultrarelativistic heavy ion collisions gives rise to polarization of direct
photons produced via gluon-quark Compton scattering, as well as by
quark-antiquark annihilation into a gluon-photon pair. We estimate the
polarization asymmetry from the Compton process within a toy model where the
polarized photons are produced from thermal gluons scattered by heavy-quark
scattering centers moving with Bjorken boost-invariant flow, and find that it
could be as large as 10%. We conclude that polarization measurements of
directly produced photons can shed light on gluon pressure anisotropy in the
early stages of collisions.
