The estimation of direction-of-arrival (DOA) angles of unknown source locations in the presence of mutual coupling (MC) is an important problem in direction finding applications. While smoothing algorithms can be used for uniform linear arrays with multiple array measurements, they cannot be applied for UCAs. Moreover, array covariance matrix is rank-deficient for single snapshot case and this leads to erroneous estimation results. In this paper, single snapshot DOA estimation in the presence of MC is considered for uniform circular arrays. A joint-sparse support recovery algorithm is proposed to estimate both DOA angles and MC coefficients. A new dictionary matrix is defined where a joint-sparse vector is constructed by embedding the spatial source directions and MC coefficients. It is shown that the proposed method performs better than the alternative sparse recovery techniques.