In this paper, we introduce and experimentally validate a simultaneous localization and mapping (SLAM) algorithm based on the processing of radar data captured in the Terahertz (THz) band. We describe a measurement campaign carried out using a dedicated setup with the purpose to investigate the main properties of the signal backscattered in an indoor environment in the THz band and assess the performance of the proposed radio-SLAM (R-SLAM) algorithm. Numerical results show that a mobile radar can track itself with high accuracy in a real scenario, without the need for any localization infrastructure, and map the surrounding environment at the same time. This validation represents one of the very first experimental characterization of THz SLAM for the automatic mapping of the indoors.