VACDensity-functional theory including spin-orbit coupling and corrections for dispersion forces has been used to investigate the structural and magnetic properties of Pt3 and Pt4 clusters deposited on a graphene layer supported on a Ni(111) substrate. It is shown that the strong interaction of the Pt atoms with the Ni-supported graphene stabilizes a flat triangular and a slightly bent rhombic structure of the clusters. Pt atoms are located nearly on top of the C atoms of the graphene layer, slightly shifted towards the bridge positions because the Pt-Pt distances are larger than the C-C distances of the graphene sheet lattice-matched to the Ni support. The strong interaction with the substrate leads to a substantial reduction of both the spin and orbital moments of the Pt atoms, not only compared to the clusters in the gas-phase, but also compared to those adsorbed on a freestanding graphene layer. The trends in the magnetic moments and in the magnetic anisotropy of the cluster/substrate complex have been analyzed and it is demonstrated that the anisotropy is dominated by the Ni support.