  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 $m_{\rm DM} \in [1,
15]$ 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.
