We present polarimetric observations of a massive pre-main sequence short-period binary star of the Herbig Ae/Be type, MWC 1080. The mean polarization at 7660 A is 1.60% at 81.6 deg, or 0.6% at 139 deg if an estimate of the interstellar polarization is subtracted. The intrinsic polarization points to an asymmetric geometry of the circumstellar or circumbinary environment while the 139 deg intrinsic position angle traces the axis of symmetry of the system and is perpendicular to the position angle of the outflow cavity. The polarization and its position angle are clearly variable, at all wavelengths, and on time scales of hours, days, months, and years. Stochastic variability is accompanied by periodic variations caused by the orbital motion of the stars in their dusty environment. These periodic polarimetric variations are the first phased-locked ones detected for a pre-main sequence binary. The variations are not simply double-periodic (seen twice per orbit) but include single-periodic (seen once per orbit) and higher-order variations. The presence of single-periodic variations could be due to non equal mass stars, the presence of dust grains, an asymmetric configuration of the circumstellar or circumbinary material, or the eccentricity of the orbit. MWC 1080 is an eclipsing binary with primary and secondary eclipses occurring at phases 0.0 and 0.55. The signatures of the eclipses are seen in the polarimetric observations.