X-ray computed tomography (CT) is one of the most commonly used three-dimensional medical imaging modalities today. It has been refined over several decades, with the most recent innovations including dual-energy and spectral photon-counting technologies. Nevertheless, it has been discovered that wave-optical contrast mechanisms-beyond the presently used X-ray attenuation-offer the potential of complementary information, particularly on otherwise unresolved tissue microstructure. One such approach is dark-field imaging, which has recently been introduced and already demonstrated significantly improved radiological benefit in small-animal models, especially for lung diseases. Until now, however, dark-field CT could not yet be translated to the human scale and has been restricted to benchtop and small-animal systems, with scan durations of several minutes or more. This is mainly because the adaption and upscaling to the mechanical complexity, speed, and size of a human CT scanner so far remained an unsolved challenge. Here, we now report the successful integration of a Talbot-Lau interferometer into a clinical CT gantry and present dark-field CT results of a human-sized anthropomorphic body phantom, reconstructed from a single rotation scan performed in 1 s. Moreover, we present our key hardware and software solutions to the previously unsolved roadblocks, which so far have kept dark-field CT from being translated from the optical bench into a rapidly rotating CT gantry, with all its associated challenges like vibrations, continuous rotation, and large field of view. This development enables clinical dark-field CT studies with human patients in the near future.