  It is widely accepted that the broad absorption line region (BALR) exists in
most (if not all) quasars with a small covering factor. Recent works showed
that the BALR is optically thick to soft and even medium energy X-rays, with a
typical hydrogen column density of a few 10$^{23}$ to $>$ 10$^{24}$ cm$^{-2}$.
The electron scattering in the thick absorber might contribute significantly to
the observed continuum polarization for both BAL QSOs and non-BAL QSOs. In this
paper, we present a detailed study of the electron scattering in the BALR by
assuming an equatorial and axisymmetric outflow model. Monte-Carlo simulations
are performed to correct the effect of the radiative transfer. Assuming an
average covering factor of 0.2 of the BALR, which is consistent with
observations, we find the electron scattering in the BALR with a column density
of $\sim$ 4 $\times$ 10$^{23}$ cm$^{-2}$ can successfully produce the observed
average continuum polarization for both BAL QSOs and non-BAL QSOs. The observed
distribution of the continuum polarization of radio quiet quasars (for both BAL
QSOs and non-BAL QSOs) is used to constrain the dispersal distribution of the
BALR. We find that, to match the observations, the maximum continuum
polarization produced by the BALR (while viewed edge-on) peaks at $P$ = 0.34%,
which is much smaller than the average continuum polarization of BAL QSOs ($P$
= 0.93%). The discrepancy can be explained by a selection bias that the BAL
with larger covering factor, and thus producing larger continuum polarization,
is more likely to be detected. A larger sample of radio quiet quasars with
accurate measurement of the continuum polarization will give better constraints
to the distribution of the BALR properties.
