A new Radial Time Projection Chamber (RTPC) was developed at the Jefferson Laboratory to track low-energy nuclear recoils to measure exclusive nuclear reactions, such as coherent deeply virtual Compton scattering and coherent meson production off 4He. In 2009, we carried out these measurements using the CEBAF Large Acceptance Spectrometer (CLAS) supplemented by the RTPC positioned directly around a gaseous 4He target, allowing a detection threshold as low as 12 MeV for 4He. This article discusses the design, principle of operation, calibration methods and performances of this RTPC.