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Radon transforms defined on smooth curves are well known and extensively studied in the literature. In this paper, we consider a Radon transform defined on a discontinuous curve formed by a pair of half‐lines forming the vertical letter V. If the classical two‐dimensional Radon transform has served as a work horse for tomographic transmission and/or emission imaging, we show that this V‐line Radon transform is the backbone of scattered radiation imaging in two dimensions. We establish its analytic inverse formula as well as a corresponding filtered back projection reconstruction procedure. These theoretical results allow the reconstruction of two‐dimensional images from Compton scattered radiation collected on a one‐dimensional collimated camera. We illustrate the working principles of this imaging modality by presenting numerical simulation results.