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A magnetic chicane bunch compressor for a new compact accelerator-based terahertz (THz) radiation source at the Institute of Advanced Energy, Kyoto University, was completely installed in March 2016. The chicane is employed to compress an electron bunch with an energy of 4.6 MeV generated by a 1.6-cell photocathode radio frequency (RF)-gun. The compressed bunch is injected into a short planar undulator for THz generation by coherent undulator radiation (CUR). The characteristics of the bunch compressor and the compressed bunch were investigated by observing the coherent transition radiation (CTR). The CTR spectra, which were analyzed by using a Michelson interferometer, and the compressed bunch length were also estimated. The results were that the chicane could compress the electron bunch at a laser injection phase less than 45 degrees, and the maximum CTR intensity was observed at a laser injection phase around 24 degrees. The optimum value of the first momentum compaction factor was around &minus, 45 mm, which provided an estimated rms bunch length less than 1 ps.