  We consider a simple abelian vector dark matter (DM) model, where {\it only}
the DM $(\widetilde{X}_\mu)$ couples non-minimally to the scalar curvature
$(\widetilde{R})$ of the background spacetime via an operator of the form $\sim
\widetilde{X}_\mu\,\widetilde{X}^\mu\,\widetilde{R}$. By considering the
standard freeze-out scenario, we show, it is possible to probe such a
non-minimally coupled DM in direct detection experiments for a coupling
strength $\xi\sim\mathcal{O}\left(10^{30}\right)$ and DM mass $m_X\lesssim 55$
TeV, satisfying Planck observed relic abundance and perturbative unitarity. We
also discuss DM production via freeze-in, governed by the non-minimal coupling,
that requires $\xi\lesssim 10^{-5}$ to produce the observed DM abundance over a
large range of DM mass depending on the choice of the reheating temperature. We
further show, even in the absence of the non-minimal coupling, it is possible
to produce the whole observed DM abundance via 2-to-2 scattering of the bath
particles mediated by massless gravitons.
