  We perform the first analysis of Dark Matter scenarios in a constrained model
with Dirac Gauginos. The model under investigation is the Constrained Minimal
Dirac Gaugino Supersymmetric Standard model (CMDGSSM) where the Majorana mass
terms of gauginos vanish. However, $R$-symmetry is broken in the Higgs sector
by an explicit and/or effective $B_\mu$-term. This causes a mass splitting
between Dirac states in the fermion sector and the neutralinos, which provide
the dark matter candidate, become pseudo-Dirac states. We discuss two
scenarios: the universal case with all scalar masses unified at the GUT scale,
and the case with non-universal Higgs soft-terms. We identify different regions
in the parameter space which fullfil all constraints from the dark matter
abundance, the limits from SUSY and direct dark matter searches and the Higgs
mass. Most of these points can be tested with the next generation of direct
dark matter detection experiments.
