We consider a simple abelian vector dark matter (DM) model, where only the DM (Xμ) couples non-minimally to the scalar curvature (R) of the background spacetime via an operator of the form 1/4Xμ Xμ 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 ζ 1/4o ‘ (1030) and DM mass m X 2 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 ζ 210-5 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.