The work presented here applies rank reduction estimator (RARE) to address the problem of two-dimensional (2D) direction-of-arrival (DOA) estimation in a computationally efficient way. Using an array of acoustic vector sensors with inter-vector-sensor nonidealities, the proposed method decouples the azimuth angle estimation from the elevation angle estimation by exploiting the unique array manifold of the acoustic vector sensor, thereby breaking 2D parameter search into two independent one-dimensional (1D) parameter search. To further reduce the computational load, the proposed method uses ESPRIT to self-generate coarse estimates of the sources' arrival angles to start off its RARE-based iterative search.