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.
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