The development of spintronics devices relies on efficient generation of spin-polarized currents and their electric-field-controlled manipulation. While observation of exceptionally long spin relaxation lengths makes graphene an intriguing material for spintronics studies, electric field modulation of spin currents is almost impossible due to negligible intrinsic spin-orbit coupling of graphene. In this work, we create an artificial interface between monolayer graphene and few-layer semiconducting tungsten disulphide. In these devices, we observe that graphene acquires spin-orbit coupling up to 17 meV, three orders of magnitude higher than its intrinsic value, without modifying the structure of the graphene. The proximity spin-orbit coupling leads to the spin Hall effect even at room temperature, and opens the door to spin field effect transistors. We show that intrinsic defects in tungsten disulphide play an important role in this proximity effect and that graphene can act as a probe to detect defects in semiconducting surfaces.