Cir X-1 is a neutron star X-ray binary characterized by strong variations in flux during its eccentric similar to 16.6 day orbit. There are also strong variations in the spectral state, and it has historically shown both atoll and Z state properties. We observed the source with the Imaging X-ray Polarimetry Explorer during two orbital segments, 6 days apart, for a total of 263 ks. We find an X-ray polarization degree in these segments of 1.6% +/- 0.3% and 1.4% +/- 0.3% at polarization angles of 37 degrees +/- 5 degrees and -12 degrees +/- 7 degrees, respectively. Thus, we observed a rotation of the polarization angle by 49 degrees +/- 8 degrees along the orbit. Because variations of accretion flow, and then of the hardness ratio, are expected during the orbit, we also studied the polarization binned in hardness ratio and found the polarization angle differing by 67 degrees +/- 11 degrees between the lowest and highest values of the hardness ratio. We discuss possible interpretations of this result that could indicate a possible misalignment between the symmetry axes of the accretion disk and the Comptonizing region caused by the misalignment of the neutron star's angular momentum with respect to the orbital one.