  We present a minimal model of fermionic dark matter (DM), where a singlet
Dirac fermion can interact with the Standard Model (SM) particles via the
torsion field of gravitational origin. In general, torsion can be realized as
an antisymmetric part of the affine connection associated with the spacetime
diffeomorphism symmetry and thus can be thought of as a massive axial vector
field. Because of its gravitational origin, the torsion field couples to all
the fermion fields including the DM with equal strength, which makes the model
quite predictive. The DM is naturally stable without any imposition of ad-hoc
symmetry {\it e.g.,} $\mathcal{Z}_2$. Apart from producing the correct thermal
abundance, singlet fermion can easily evade the stringent bounds on the
spin-independent DM-nucleon direct detection cross-section due to its axial
nature. However, in the allowed parameter space, strong bounds can be placed on
the torsion mass and its couplings to fermions from the recent LHC searches.
Assuming a non universal torsion-DM and torsion-SM coupling, smaller values of
torsion masses may become allowed. In both cases we also study the reach of
spin-dependent direct detection searches of the DM.
