As an image processing technology, edge enhancement has important applications for studying the boundary information of objects. According to the correlation theory of thermal light ghost imaging, a phase object edge enhancement recognition system was established by combining the ghost imaging with the spiral phase contrast imaging technology. The phase object and the vortex filter were placed in the signal and idle optical path of the ghost imaging system non-locally. The results prove that by using the vortex filter with the fractional orbital angular momentum (OAM) from 0 to 1, the gradual edge enhancement of the phase object can be realized. The higher the OAM topological charge, the more obvious edge enhancement effect will be. Compared with the traditional spiral phase contrast imaging scheme, the limitation of the filter in the spatial frequency spectrum in the spectral plane is broken by the non-local spiral phase contrast imaging scheme. In addition, the coherence requirement of the active illumination light source is released, and the generalization ability of the spiral phase contrast imaging system is enhanced.