We obtained optical imaging polarimetry with the ACS/HRC aboard the HST of the 9 closest radio-galaxies in the 3C catalogue with an FR I morphology. The nuclear sources seen in direct HST images in these galaxies are found to be highly polarized with levels in the range ~2-11 % with a median value of 7 %. We discuss the different mechanisms that produce polarized emission and conclude that the only viable interpretation is a synchrotron origin for the optical nuclei. This idea is strengthened by the analogy with the polarization properties of BL Lac objects, providing also further support to the FRI/BL Lac unified model. This confirms previous suggestions that the dominant emission mechanism in low luminosity radio-loud AGN is related to non-thermal radiation produced by the base of their jets. In addition to the nuclear polarization (and to the large scale optical jets), polarization is detected co-spatially with the dusty circumnuclear disks, likely due to dichroic transmission; the polarization vectors are tangential to the disks as expected when the magnetic field responsible for the grains alignment is stretched by differential rotation. We explored the possibility to detect the polarimetric signature of a misaligned radiation beam in FR I, expected in our sources in the frame of the FR I/ BL Lac unification. We did not find this effect in any of the galaxies, but our the results are not conclusive on whether a misaligned beam is indeed present in FR I.