We study compressive sensing methods for target localization in MIMO radar. While much attention has been given to compressive sensing of signal measurements in the time domain, this work focuses on the spatial domain. We propose a framework in which the target localization with distributed, active sensors is formulated as a nonconvex optimization. By leveraging a sparse representation, we devise a branch-and-bound type algorithm that provides a global solution to the nonconvex localization problem. It is shown that this method can achieve high resolution target localization with a highly undersampled MIMO radar with transmit/receive elements placed at random. A lower bound is developed on the number of required transmit/receive elements required to ensure accurate target localization with high probability.