  We consider dark matter (DM) that interacts with ordinary matter exclusively
through an electromagnetic anapole, which is the only allowed electromagnetic
form factor for Majorana fermions. We show that unlike DM particles with an
electric or magnetic dipole moment, anapole dark matter particles annihilate
exclusively into fermions via purely p-wave interactions, while tree-level
annihilations into photons are forbidden. We calculate the anapole moment
needed to produce a thermal relic abundance in agreement with cosmological
observations, and show that it is consistent with current XENON100 detection
limits on the DM-nucleus cross-section for all masses, while lying just below
the detection threshold for a mass ~ 30-40 GeV.
