  It is well-known since the works of Utiyama and Kibble that the gravitational
force can be obtained by gauging the Poincar\'e group, which puts gravity on
the same footing as the Standard Model fields. The resulting theory --
Einstein-Cartan gravity -- inevitably contains four-fermion and scalar-fermion
interactions that originate from torsion associated with spin degrees of
freedom. We show that these interactions lead to a novel mechanism for
producing singlet fermions in the Early Universe. These fermions can play the
role of dark matter particles. The mechanism is operative in a large range of
dark matter particle masses: from a few keV up to $\sim 10^8~$GeV. We discuss
potential observational consequences of keV-scale dark matter produced this
way, in particular for right-handed neutrinos. We conclude that a determination
of the primordial dark matter momentum distribution might be able to shed light
on the gravity-induced fermionic interactions.
