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The observable signal of higher-spin particles is rare in current particlecollider experiments. In the meantime, there have no evident constraints on thespin of the dark matter particles. And thereby it is natural to consider thepossibility that the higher-spin particles behaves as dark matter. In thiswork, we investigate the direct detection of (spin-$3/2$) gravitino dark matterand (spin-$2$) massive KK-graviton dark matter respectively through theDM-electron scattering. Both the spin-independent (SI) and spin-independent(SD) interactions of DM are considered. Using the experiment datas of XENON10,XENON100 and XENON1T, we could give the restriction relation between the DMmass and cross section. For simplification, we only compute the corss sectionat leading order, while merely focus on the (pseudo)scalar mediators. Moreover,by evaluating and analyzing the form factor of DM, we uncover that if themediator is scalar there have no significant signals to distinguish the DM withspin $3/2,2$ from the one with spin $0,1/2,1$.

Direct Detection of Sub-GeV Dark Matter with $s>1$ through the  DM-Electron Scattering (I): case study for $s=3/2$ and $s=2$ with  (pseudo)scalar mediator