In this paper, we propose a low complexity direction of arrival (DoA) estimation algorithm that operates in radio frequency (RF) lens-embedded millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems. In mmWave system, to compute the beamforming weighting coefficients in real-time, precise DoA estimation with low complexity is essential. We first investigate the conventional DoA estimation algorithms in mmWave MIMO systems and evaluate its performance. Then we introduce the Power pROfile Based Estimation (PROBE) algorithm for DoA estimation that operates in the RF lens-embedded system. We elaborate on the computational complexity of each algorithm in terms of the number of multiplication operations. We show that the proposed algorithm has a significant performance advantage in terms of estimation accuracy over other conventional algorithms in a complexity-constrained environment.