A mechanism for the high-precision positioning of reflector segments by using kinematic couplings has been developed for balloon-borne radio telescopes, and the effectiveness of the mechanism is demonstrated through experiments. A high-precision reflector for radio telescopes is under development, and it is intended to be used for the observation of radio waves of up to 300 GHz. The reflector consists of six segments, a back structure, and a high-precision positioning mechanism. The high-precision positioning mechanism utilizes kinematic couplings, and the segments are positioned and fixed precisely to the back structure by the kinematic couplings. The positioning of the segments on the back structure is one of the largest sources of error in reflector systems. Therefore, kinematic couplings are important components of a reflector system for achieving a high surface accuracy. Three combinations of a ball and a V-groove are employed in the positioning mechanism. Load-applying mechanisms are used to apply and control pressing loads between the segment and back structure. In order to demonstrate the effectiveness of the mechanism, the positioning repeatability between a segment and a back structure was investigated through experiments. In these experiments, the reflector segment was attached to and detached from the back structure, and the relative positions of the reflector with respect to the back structure were measured using a photogrammetry system during the process of attachment. The cycle of attachment, measurement, and detachment was repeated five times, and the positioning repeatability was evaluated. A positioning accuracy of approximately 20 um RMS was achieved using the developed reflector system. The results demonstrate the effectiveness of the positioning mechanism, which incorporates kinematic couplings for the high-precision positioning of a reflector for a balloon-borne radio telescope.