We demonstrate the integration of a single-crystal magneto-optical film onto thin silicon-on-insulator (SOI) waveguides by use of direct wafer bonding. Simulations show that the high confinement and asymmetric structure of SOI allows an enhancement of approximately 3x over the nonreciprocal phase shift achieved in previous designs; this value is confirmed by our measurements. Our structure will allow compact magneto-optical nonreciprocal devices, such as isolators, integrated on a silicon waveguiding platform.