  The circular polarization of gravitational waves is a powerful observable to
test parity violation in gravity and to distinguish between the primordial or
the astrophysical origin of the stochastic background. This property comes from
the expected unpolarized nature of the homogeneous and isotropic astrophysical
background, contrary to some specific cosmological sources that can produce a
polarized background. However, in this work we show that there is a
non-negligible amount of circular polarization also in the astrophysical
background, generated by Poisson fluctuations in the number of unresolved
sources, which can be detected by the third-generation interferometers with
signal-to-noise ratio larger than one. We also explain in which cases the
gravitational wave maps can be cleaned from this extra source of noise,
exploiting the frequency and the angular dependence, in order to search for
signals from the early Universe. Future studies about the detection of
polarized cosmological backgrounds with ground- and space-based interferometers
should account for the presence of such a foreground contribution.
