We propose and experimentally demonstrate an on-axis phase-shifting correlation holography technique with un-polarized light. The randomness of the un-polarized light is exploited to evaluate the higher-order polarization correlation and to consequently apply it in the reconstruction of the hologram from the randomness. A detailed theoretical analysis is developed and verified by numerical simulations and followed by experimental demonstrations. To validate the application of the proposed technique, imaging of different helical phase objects with randomness is presented. A good affinity is found between simulation and experimental results, which validates the accuracy of the proposed technique.