  We systematically study the possibilities for asymmetric dark matter in the
context of non-supersymmetric SO(10) models of grand unification. Dark matter
stability in SO(10) is guaranteed by a remnant $\mathbb{Z}_2$ symmetry which is
preserved when the intermediate scale gauge subgroup of SO(10) is broken by a
${\bf 126}$ dimensional representation. The asymmetry in the dark matter states
is directly generated through the out-of-equilibrium decay of particles around
the intermediate scale, or transferred from the baryon/lepton asymmetry
generated in the Standard Model sector by leptogenesis. We systematically
classify possible asymmetric dark matter candidates in terms of their quantum
numbers, and derive the conditions for each case that the observed dark matter
density is (mostly) explained by the asymmetry of dark matter particles.
