This letter investigates the non-coherent Direction of Arrival (DOA) estimation problem dealing with the DOA estimation from magnitude only measurements of the array output. The magnitude squared of the array output is expanded as a superposition of some harmonics. Hence, a frequency estimation approach is used to find some nonlinear relations between DOAs, which results in inherent ambiguities. To solve the nonlinear equations and resolve the ambiguities, we assume a high amplitude reference target at low angles to estimate the true DOA's with no ambiguities. However, the proposed algorithm requires a large number of antenna array elements to accurately estimate the DOA's. To overcome this drawback, and to enhance the estimation accuracy, we suggest two variants of the algorithm. One is to add virtual elements in the array and the second is to integrate multiple snapshots. Simulation results show that the proposed frequency estimation-based algorithm outperforms the non-coherent GESPAR algorithm in the low signal to noise ratio (SNR) regime and it is two orders of magnitude faster than the non-coherent GESPAR algorithm.