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In this paper, we consider the problem of estimating direction of arrivals (DOA) using a single snapshot of sparse linear array (SLA); the employed SLA is a sampled version of a uniform linear array (ULA). For the estimation task, we propose a two-step algorithm: (i) we first interpolate for the missing samples of the SLA to form a complete ULA by converting the samples into Hankel matrix and solving a weighted low-rank minimization. (ii) Next, we estimate the DOAs using a subspace method, like Prony. In step (i), the matrix completion problem is approached by adding left and right weight matrices to the Hankel matrix obtained by lifting the antenna observations. Simulation results show that the proposed method has superior accuracy in DOA estimation compared to the other methods proposed in the literature, such as atomic-norm minimization and off-the-grid approaches.