Methods to measure the polarization of x rays from highly charged heavy ions with a significantly higher accuracy than that of the existing technology are needed to explore relativistic and quantum electrodynamics effects, including the Breit interaction. We developed an Electron Beam Ion Trap Compton Camera (EBIT-CC), a new Compton polarimeter with pixelated multi-layer silicon, and cadmium telluride counters. The EBIT-CC detects the three-dimensional position of Compton scattering and photoelectric absorption, and thus, the degree of polarization of incoming x rays can be evaluated. We attached the EBIT-CC on the Tokyo Electron Beam Ion Trap (Tokyo-EBIT) in the University of Electro-Communications. An experiment was performed to evaluate its polarimetric capability through an observation of radiative recombination x rays emitted from highly charged krypton ions, which were generated by the Tokyo-EBIT. The CC of the EBIT-CC was calibrated for the ∼75 keV x rays. We developed event reconstruction and selection procedures and applied them to every registered event. As a result, we successfully obtained the polarization degree with an absolute uncertainty of 0.02. This uncertainty is small enough to probe the difference between the zero-frequency approximation and full-frequency-dependent calculation for the Breit interaction, which is expected for dielectronic recombination x rays of highly charged heavy ions.