Centaurus A is one of the closest radio-galaxies to Earth. Its proximity allowed us to extensively study its active galactic nucleus but the core emission mechanism remains elusive because of local strong dust and gas obscuration. The capability of polarimetry to shave-off contaminating emission has been exploited without success in the near-infrared by previous studies but the very recent measurement of the 2 - 8 keV polarization by the Imaging X-ray Polarimetry Explorer (IXPE) brought the question back to the fore. To determine what is the prevalent photon generation mechanism to the multi-wavelength emission from the core of Centaurus A, we retrieved from the archives the panchromatic polarization measurements of the central compact component. We built the total and polarized flux spectral energy distributions of the core and demonstrated that synchrotron self-Compton models nicely fit the polarized flux from the radio to the X-ray band. The linear polarization of the synchrotron continuum is perpendicular to the jet radio axis from the optical to the radio band, and parallel to it at higher energies. The observed smooth rotation of the polarization angle in the ultraviolet band is attributed to synchrotron emission from regions that are getting closer to the particle acceleration site, where the orientation of the jet's magnetic fields become perpendicular to the jet axis. This phenomenon support the shock acceleration mechanism for particle acceleration in Centaurus A, in line with IXPE observations of several high-synchrotron peak blazars.