  We compute the photon emission rate from a quark-gluon plasma with an
anisotropic particle momentum distribution induced by a non-vanishing local
shear pressure tensor. Our calculation includes photon production through
Compton scattering and quark-antiquark annihilation at leading order in
$\alpha_s$, with all off-equilibrium corrections to leading order in the
momentum anisotropy. For fermions we prove that the Kubo-Martin-Schwinger (KMS)
relation holds in the hard loop regime for any particle momentum distribution
function that is reflection-symmetric. This supports the equivalence, for 2 to
2 scattering processes, of the diagrammatic and kinetic approaches to
calculating the photon emission rate. We compare the viscous rates from these
two approaches at weak and realistic coupling strengths and provide
parameterizations of the equilibrium and viscous photon emission rates for
phenomenological studies in relativistic heavy-ion collisions.
