Van der Waals growth of GaAs on silicon using a two-dimensional layered material, graphene, as a lattice mismatch/thermal expansion coefficient mismatch relieving buffer layer is presented. Two-dimensional growth of GaAs thin films on graphene is a potential route towards heteroepitaxial integration of GaAs on silicon in the developing field of silicon photonics. Hetero-layered GaAs is deposited by molecular beam epitaxy on graphene/silicon at growth temperatures ranging from 350 degrees C to 600 degrees C under a constant arsenic flux. Samples are characterized by plan-view scanning electron microscopy, atomic force microscopy, Raman microscopy, and X-ray diffraction. The low energy of the graphene surface and the GaAs/graphene interface is overcome through an optimized growth technique to obtain an atomically smooth low temperature GaAs nucleation layer. However, the low adsorption and migration energies of gallium and arsenic atoms on graphene result in cluster-growth mode during crystallization of GaAs films at an elevated temperature. In this paper, we present the first example of an ultrasmooth morphology for GaAs films with a strong (111) oriented fiber-texture on graphene/silicon using quasi van der Waals epitaxy, making it a remarkable step towards an eventual demonstration of the epitaxial growth of GaAs by this approach for heterogeneous integration.