The integration of complex oxides on silicon presents opportunities to extend and enhance silicon technology with novel electronic, magnetic, and photonic properties. Among these materials, barium titanate (BaTiO3) is a particularly strong ferroelectric perovskite oxide with attractive dielectric and electro-optic properties. Here we demonstrate nanophotonic circuits incorporating ferroelectric BaTiO3 thin films on the ubiquitous silicon-on-insulator (SOI) platform. We grow epitaxial, single-crystalline BaTiO3 directly on SOI and engineer integrated waveguide structures that simultaneously confine light and an RF electric field in the BaTiO3 layer. Using on-chip photonic interferometers, we extract a large effective Pockels coefficient of 213 plus minus 49 pm/V, a value more than six times larger than found in commercial optical modulators based on lithium niobate. The monolithically integrated BaTiO3 optical modulators show modulation bandwidth in the gigahertz regime, which is promising for broadband applications.