  We study linear polarization of optical emission from white dwarf (WD) binary
system AR~Scorpii. The optical emission from this binary is modulating with the
beat frequency of the system, and it is highly polarized, with the degree of
the polarization reaching $\sim 40$\%. The angle of the polarization
monotonically increases with the spin phase, and the total swing angle can
reach $360^{\circ}$ over one spin phase. It is also observed that the
morphology of the pulse profile and the degree of linear polarization evolve
with the orbital phase. These polarization properties can constrain the
scenario for nonthermal emission from AR Scorpii. In this paper, we study the
polarization properties predicted by the emission model, in which (i) the
pulsed optical emission is produced by the synchrotron emission from
relativistic electrons trapped by magnetic field lines of the WD and (ii) the
emission is mainly produced at magnetic mirror points of the electron motion.
We find that this model can reproduce the large swing of the polarization
angle, provided that the distribution of the initial pitch angle of the
electrons that are leaving the M-type star is biased to a smaller angle rather
than a uniform distribution. The observed direction of the swing suggests that
the Earth viewing angle is less than $90^{\circ}$ measured from the WD spin
axis. The current model prefers an Earth viewing angle of
$50^{\circ}-60^{\circ}$ and a magnetic inclination angle of
$50^{\circ}-60^{\circ}$ (or $120^{\circ}-130^{\circ}$). We discuss that the
different contribution of the emission from M-type star to total emission
causes a large variation in the pulsed fraction and the degree of the linear
polarization along the orbital phase.
