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.

7 pages, 5 figures, v3: version to appear in PLB