  The cosmic infrared background (CIB) is slightly polarized. Polarization
directions of individual galaxies could be aligned with tidal fields around
galaxies, resulting in nonzero CIB polarization. We use a linear intrinsic
alignment model to theoretically predict angular correlations of the CIB
polarization fluctuations and find that electriclike and curl-like ($B$-mode)
polarization modes are equally generated with power four orders of magnitude
less than its intensity. The CIB $B$-mode signal is negligible and not a
concerning foreground for the inflationary $B$-mode searches at nominal
frequencies for cosmic microwave background measurements, but could be detected
at submillimetre wavelengths by future space missions.
