We present the results of simultaneous UBVRI photometry and polarimetry of the classical T Tauri star CO Ori carried out at the Crimean Astrophysical Observatory during the 18 years between 1986 and 2004. We show that the variations of linear polarization accompanying the star's brightness variations follow the law characteristic of UX Ori stars. This suggests that the brightness variations of the star are mainly due to changes of the circumstellar extinction due to non-uniform structure of the circumstellar environment, and to an "optimal" orientation of the circumstellar gas and dust disk relative to the observer, whose line of sight crosses the gas and dust atmosphere of the disk. We determine the star's intrinsic polarization due to scattering of light in the circumstellar disk. The polarization position angle indicates the orientation of the disk's symmetry axis in the plane of the sky. Our analysis of an archival light curve for CO Ori confirms the existence of a many-year cycle of photometric activity, suspected by us earlier. The refined period of this cycle is 12.4 years. The existence of such activity cycles of UX Ori stars testifies to considerable deviations of their circumstellar disks from axial symmetry, a reflection of either stellar binarity or the commencement of the process of planetary formation.