We propose a experimental scenario of edge enhancement ghost imaging of phase objects with nonlocal orbital angular momentum (OAM) phase filters. Spatially incoherent thermal light is separated into two daughter beams, the test and reference beams, in which the detected objects and phase filters are symmetrically placed,respectively. The results of simulation experiment prove that the edge enhanced ghost images of phase objects can be achieved through the second-order light field intensity correlation measurement owing to the OAM correlation characteristics. Further simulation results demonstrate that the edge enhanced ghost imaging system dose not violate a Bell-type inequality for the OAM subspace, which reveals the classical nature of the thermal light correlation.