We present a Fourier-based approach for source direction-of-arrival (DOA) estimation that exploits all degrees-of-freedom offered by a co-prime array. The proposed technique is an extension of the fast iterative interpolated beamforming (FIIB), which is a low-complexity algorithm for DOA estimation using uniform linear arrays. We design modifications to the FIIB to account for the non-uniformity of the co-prime array. Performance validation of the proposed approach is provided using numerical results.