  If dark matter interactions with Standard Model particles are $CP$-violating,
then dark matter annihilation/decay can produce photons with a net circular
polarization. We consider the prospects for experimentally detecting evidence
for such a circular polarization. We identify optimal models for dark matter
interactions with the Standard Model, from the point of view of detectability
of the net polarization, for the case of either symmetric or asymmetric dark
matter. We find that, for symmetric dark matter, evidence for net polarization
could be found by a search of the Galactic Center by an instrument sensitive to
circular polarization with an efficiency-weighted exposure of at least
$50000~\text{cm}^2~\text{yr}$, provided the systematic detector uncertainties
are constrained at the $1\%$ level. Better sensitivity can be obtained in the
case of asymmetric dark matter. We discuss the prospects for achieving the
needed level of performance using possible detector technologies.
