In this work, we propose a new algorithm in order to perform direction-of-arrival (DOA) estimation considering waves propagating through a fluctuating medium. In this particular context, the measurements are affected by a phase noise, which can mislead the estimation. It is then important to take into account these phase uncertainties in the estimation procedures. In this paper, we propose to model the phase noise by some random distribution and combine it with a sparse-enforcing distribution on the directions of arrival. These prior models are exploited through a message passing algorithm. Our method relates to previous works in phase recovery and can be seen in particular as an extension of the so-called " prSAMP " algorithm. Once implemented, we evaluated the performance of our algorithm in terms of quality of the reconstruction in comparison with other state-of-the-art algorithms. In particular, the method proves to be more robust to additive noise and present a better behavior than conventional beamforming and recent variational Bayesian algorithms.