In this paper, we propose a plasmonic tetramer composed of coupled graphene nanodisks. The transformation from the isolated to the collective modes of the proposed structure is investigated by analysing the whispering-gallery modes and extinction spectra with various inter-nanodisk gap distances. In addition, the effect of introducing a central nanodisk into the tetramer on the extinction spectra is explored, which leads to Fano resonance. Furthermore, the refractive index sensing properties of the proposed graphene plasmonic oligomer have been demonstrated. The proposed nanostructures might pave the road toward the application of graphene plasmonic oligomers in fields such as nanophotonics, and chemical or biochemical sensing.