In a ferroelectric memristor, the manifestation of resistive effects is most often associated with the influence of polarization and dynamics of the domain structure on the charge transport. The role of point defects is either not taken into account or is reduced to the modulation of potential barriers at the interfaces with electrodes. However, the similarity of charge transport mechanisms in memristors based on thin ferroelectric and metal-oxide films suggests that the contribution of point defects in the anionic sublattice, namely, oxygen vacancies, to the resistive switching in ferroelectric memristors may be dominant. In order to identify the key factors responsible for resistive tuning in a ferroelectric memristor, a combined experimental and theoretical study of resistive switching effects in 10-nm polycrystalline barium titanate films was performed. X-ray photoelectron spectroscopy, piezoresponse force microscopy and scanning tunneling microscopy were employed to investigate the local resistive and ferroelectric properties and to estimate the stoichiometry of the films. A drift-diffusion numerical model of non-stationary processes in thin ferroelectric films was developed, including the Poisson equation and the continuity equation for each component of mobile charge carriers. Using the developed model as well as experimental I—V characteristics taken with scanning tunneling spectroscopy, the contribution of various mechanisms to the resistive switching in ferroelectric memristors with polycrystalline barium titanate has been studied. Non-stationary processes involving oxygen vacancies were found to govern the resistive switching.