  We study the loop-induced circularly polarized gamma rays from dark matter
annihilation using the effective dark matter theory approach. Both neutral
scalar and fermionic dark matter annihilating into monochromatic diphoton and
$Z$-photon final states are considered. To generate the circular polarization
asymmetry, $P$ and $CP$ symmetries must be violated in the couplings between
dark matter and Standard Model fermions inside the loop with non-vanishing
Cutkosky cut. The asymmetry can be sizable especially for $Z$-photon final
state for which asymmetry of nearly $90\%$ can be reached. We discuss the
prospect for detecting the circular polarization asymmetry of the gamma-ray
flux from dark matter annihilation in the Galactic Center in future gamma-ray
polarimetry experiments.

High Energy Physics - Phenomenology;High Energy Astrophysical Phenomena