  To detect and track structural changes in atomic nuclei, the systematic study
of nuclear levels with firm spin-parity assignments is important. While linear
polarization measurements have been applied to determine the electromagnetic
character of gamma-ray transitions, the applicable range is strongly limited
due to the low efficiency of the detection system. The multi-layer
Cadmium-Telluride (CdTe) Compton camera can be a state-of-the-art gamma-ray
polarimeter for nuclear spectroscopy with the high position sensitivity and the
detection efficiency. We demonstrated the capability to operate this detector
as a reliable gamma-ray polarimeter by using polarized 847-keV gamma rays
produced by the $^{56}\rm{Fe}({\it p},{\it p'}\gamma)$ reaction. By combining
the experimental data and simulated calculations, the modulation curve for the
gamma ray was successfully obtained. A remarkably high polarization sensitivity
was achieved, compatible with a reasonable detection efficiency. Based on the
obtained results, a possible future gamma-ray polarimetery is discussed.
