We study the possibility that Dark Matter (DM) particles of spin 0, 1/2 or 1 may interact gravitationally with Standard Model (SM) particles within the framework of a warped Randall–Sundrum (RS) model. Both the Dark Matter and the Standard Model particles are assumed to be confined to the infra-red (IR) brane and only interchange Kaluza–Klein excitations of the graviton and the radion (adopting the Goldberger–Wise mechanism to stabilize the size of the extra-dimension). We analyze the different DM annihilation channels and find that the presently observed Dark Matter relic abundance, $$\Omega _{\mathrm{DM}}$$ ${\Omega }_{\mathrm{DM}}$ , can be obtained within the freeze-out mechanism for DM particles of all considered spins. This extends our first work concerning scalar DM in RS scenarios (Folgado et al., in JHEP 01:161. https://doi.org/10.1007/JHEP01(2020)161 , 2020) and put it on equal footing with our second work in which we studied DM particles of spin 0, 1/2 and 1 in the framework of the Clockwork/Linear Dilaton (CW/LD) model (Folgado et al., in JHEP 20:036. https://doi.org/10.1007/JHEP04(2020)036 , 2020). We study the region of the model parameter space for which $$\Omega _{\mathrm{DM}}$$ ${\Omega }_{\mathrm{DM}}$ is achieved and compare it with the different experimental and theoretical bounds. We find that, for DM particles mass $$m_{\mathrm{DM}} \in [1,15]$$ $m_{\mathrm{DM}}\in [1,15]$ TeV, most of the parameter space is excluded by the current constraints or will be excluded by the LHC Run III or by the LHC upgrade, the HL-LHC. The observed DM relic abundance can still be achieved for DM masses $$m_{\mathrm{DM}} \in [4,15]$$ $m_{\mathrm{DM}}\in [4,15]$ TeV and $$m_{G_1} < 10$$ $m_{G_1}<10$ TeV for scalar and vector boson Dark Matter. On the other hand, for spin 1/2 fermion Dark Matter, only a tiny region with $$m_{\mathrm{DM }} \in [4, 15]$$ $m_{\mathrm{DM}}\in [4,15]$ TeV, $$m_{G_1} \in [5,10]$$ $m_{G_1}\in [5,10]$ TeV and $$\Lambda > m_{G_1}$$ $\Lambda >m_{G_1}$ is compatible with theoretical and experimental bounds. We have also studied the impact of the radion in the phenomenology, finding that it does not modify significantly the allowed region for DM particles of any spin (differently from the CW/LD case, where its impact was quite significant in the case of scalar DM). We, eventually, briefly compare results in RS with those obtained in the CW/LD model.