Polarization is indicative of material anisotropy, a property that reveals structural orientation information of molecules inside the material. Herein we investigate whether polarization can be detected optoacoustically in scattering and absorbing tissues. Using a laboratory prototype of polarization-sensitive optoacoustic tomography, we demonstrate high-resolution reconstructions of dichroism contrast deep in optically diffusive tissue-mimicking phantoms. The technique is expected to enable highly accurate imaging of polarization contrast in tissues, far beyond the current capabilities of pure optical polarization-imaging approaches.