Ferroelectric materials are characterized by a permanent electric dipole that can be reversed through the application of an external voltage, but a strong intrinsic coupling between polarization and deformation also causes all ferroelectrics to be piezoelectric, leading to applications in sensors and high-displacement actuators. A less explored property is flexoelectricity, the coupling between polarization and a strain gradient. We demonstrate that the stress gradient generated by the tip of an atomic force microscope can mechanically switch the polarization in the nanoscale volume of a ferroelectric film. Pure mechanical force can therefore be used as a dynamic tool for polarization control and may enable applications in which memory bits are written mechanically and read electrically.