  The Dirac nature of the gauginos (and also the Higgsinos) can be realized in
$R$-symmetric supersymmetry models. In this class of models, the Dirac bino (or
wino) with a small mixture of the Dirac Higgsinos is a good dark matter
candidate. When the seesaw mechanism with Higgs triplet superfields is
implemented to account for the neutrino masses and mixing, the leptogenesis
driven by the heavy triplet decay is shown to produce not only the
matter-antimatter asymmetry but also the asymmetric relic density of the Dirac
gaugino dark matter. The dark matter mass turns out to be controlled by the
Yukawa couplings of the heavy Higgs triplets, and it can be naturally at the
weak scale for a mild hierarchy of the Yukawa couplings.
