  X-ray binaries hosting a compact object have been among the main targets of
the Imaging X-ray Polarimetry Explorer (IXPE) since its launch, due to their
high brightness in the 2-8 keV energy band. The spectropolarimetric analysis
performed so far has proved to be of great importance in providing constraints
on the accretion geometry of these systems. However, the data statistics is not
enough to unambiguously disentangle the contribution of the single components
to the net observed polarimetric signal. In this work, we aim to present a
model for computing the polarization degree and polarization angle of the
boundary layer around weakly magnetized neutron stars in low-mass X-ray
binaries in the soft state. The main motivation is to provide strong
theoretical support to data interpretation of observations performed by IXPE or
future satellites for X-ray polarimetry. The results were obtained by modeling
the boundary layer as an equatorial belt around the compact object and locally
approximating it as a plane-parallel scattering atmosphere, for which the
associated radiative transfer equation for polarized radiation in the Thomson
limit was solved. The polarimetric quantities were then transformed from the
comoving frame to the observer frame using the numerical methods formerly
developed for X-ray pulsars. For typical values of the optical depth and
electron temperature of the boundary layer of these systems in a soft state,
the polarization degree was less then 0.5\%, while the polarization angle was
rotated by $\protect \la 5^{\circ}$ with respect to the neutron star spin axis
due to special and general relativistic effects for fast rotation, the amount
progressively decreasing for lower spin frequencies. The derived quantities can
be used to remove degeneracy when multicomponent spectropolarimetry is
performed.
