Ultrasound computed tomography (UCT) allows the reconstruction of quantitative tissue characteristics, such as speed of sound, mass density, and attenuation. Lowering its acquisition time would be beneficial; however, this is fundamentally limited by the physical time of flight and the number of transmission events. In this letter, we propose a compressed sensing solution for UCT. The adopted measurement scheme is based on compressed acquisitions, with concurrent randomised transmissions in a circular array configuration. Reconstruction of the image is then obtained by combining the born iterative method and total variation minimization, thereby exploiting variation sparsity in the image domain. Evaluation using simulated UCT scattering measurements shows that the proposed transmission scheme performs better than uniform undersampling, and is able to reduce acquisition time by almost one order of magnitude, while maintaining high spatial resolution.