Abstract: We study for the first time the possibility that Dark Matter (represented by particles with spin 0, 1/2 or 1) interacts gravitationally with Standard Model particles in an extra-dimensional Clockwork/Linear Dilaton model. We assume that both, the Dark Matter and the Standard Model, are localized in the IR-brane and only interact via gravitational mediators, namely the Kaluza-Klein (KK) graviton and the radion/KK-dilaton modes. We analyse in detail the Dark Matter annihilation channel into Standard Model particles and into two on-shell Kaluza-Klein towers (either two KK-gravitons, or two radion/KK- dilatons, or one of each), finding that it is possible to obtain the observed relic abundance via thermal freeze-out for Dark Matter masses in the range m(DM) is an element of [1, 15] TeV for a 5- dimensional gravitational scale M-5 ranging from 5 to a few hundreds of TeV, even after taking into account the bounds from LHC Run II and irrespectively of the DM particle spin.