Direction-of-arrival (DoA) estimation plays a critical role in applications of acoustic localization. This work proposes a closed-form algorithm for single-source one-dimensional direction of arrival estimation using the uniform circular array. The algorithm estimates the azimuthal direction of arrival using the least-square estimate of the circular harmonics steering vector. The least-square (LS) estimate of the steering vector is estimated as the principal eigenvector of the received data covariance matrix. The proposed algorithm is tested and compare against the time-frequency circular harmonics beamforming (TF-CHB) and eigenbeam MUSIC (EB-MUSIC) algorithms. The comparison shows that the proposed algorithm outperformed the two benchmark methods in accuracy under various test conditions.