Ferroelectric oxide memristors are currently in the highlights of a thriving area of research aiming at the development of nonvolatile, adaptive memories for applications in neuromorphic computing. However, to date a precise control of synapse-like functionalities by adjusting the interplay between ferroelectric polarization and resistive switching processes is still an ongoing challenge. Here, it is shown that by means of controlled electron beam radiation, a prototypical ferroelectric film of BaTiO3 can be turned into a memristor with multiple configurable resistance states. Ex situ and in situ analyses of current/voltage characteristics upon electron beam exposure confirm the quasi-continuous variation of BaTiO3 resistance up to two orders of magnitude under the typical experimental conditions employed in electron beam patterning and characterization techniques. These results demonstrate an unprecedented effective route to locally and scalably engineering multilevel ferroelectric memristors via application of moderate electron beam radiation.