The emergence of optical vortex phenomena has generated significant interest in optical technologies. By manipulating light parameters such as amplitude, phase, and polarization, new advances have been made in structured light techniques, which enable the creation of phase and polarization singularity. The present work demonstrates a novel and robust technique for converting phase singularity into polarization singularity through single-pass phase modulation of the input beam. The proposed approach simplifies the experimental setup and enables flexibility in the generation of different forms of polarization singularity, including topological conversion from C-point to V-point polarization singularity or otherwise. The method can be useful for diverse applications of singular beams, such as for classical and quantum information processing, and communications.