Polymer glasses such as the plastics used in pipes, structural materials, and medical devices are ubiquitous in daily life. The nature of their low molecular mobility is still poorly understood and it leads to brittle mechanical behavior, damage, and fracture over time. It also prevents the design of self-healing mechanisms that expand the material's lifespan, as more commonly done in recent years for higher mobility amorphous polymers such as gels and rubbers. We demonstrate through numerical simulations that controlled oscillatory deformations enhance the local molecular mobility of glassy polymers without compromising their structural or mechanical stability. We apply this principle to increase the molecular mobility around the surface of a cylindrical crack, counterintuitively inducing fracture repair and recovering the mechanical properties of the pristine material. Our findings are a first step to establish a general physical mechanism of self-healing in glasses that may inspire the design and processing of new glassy materials. Amorphous glassy materials do not usually heal damage spontaneously due to their low molecular mobility. Here, the authors show via molecular dynamics simulations that oscillatory deformations of the right frequency and amplitude can accelerate glassy dynamics, promoting molecular flow and damage repair.