One-bit direction-of-arrival (DoA) estimation has drawn considerable attention in recent years with the increasing demand for low power consumption and high sampling rate. In this work, the 1-bit DoA estimation for deterministic signals is addressed from the viewpoint of sparse matrix recovery. First, using maximum likelihood (ML) and compressive sensing techniques, 1-bit DoA estimation is formulated as an ML-based row sparse matrix optimization in terms of least-absolute-shrinkage-and-selection-operator form with an ℓ2,1 regularization. After that, by complex-valued conjugate gradient and steepest descent operations, an iterative closed-form solution in the form of a row-sparse matrix is expected to be obtained. At last, the estimates of source numbers and DoAs are simultaneously completed by making sense of the structure of the row-sparse matrix. Numerical results showcase that the proposed algorithm outperforms the state-of-the-art approaches in terms of estimation accuracy.