When an azobenzene-containing polymer film is exposed to non-uniform illumination, a light-induced mass migration process may be induced, leading to the formation of relief patterns on the polymer-free surface. Despite many years of research effort, several aspects of this phenomenon remain poorly understood. Here we report the appearance of spiral-shaped relief patterns on the polymer film under the illumination of focused Laguerre-Gauss beams with helical wavefronts and an optical vortex at their axis. The induced spiral reliefs are sensitive to the vortex topological charge and to the wavefront handedness. These findings are unexpected because the doughnut-shaped intensity profile of Laguerre-Gauss beams contains no information about the wavefront handedness. We propose a model that explains the main features of this phenomenon through the surface-mediated interference of the longitudinal and transverse components of the optical field. These results may find applications in optical nanolithography and optical-field nanoimaging.