Symbiotic stars, believed to be binary systems of a mass-losing giant and a white dwarf with an emission nebula, are known to exhibit very broad wings around Hex that extend to $~10^3km;s^{-1}$. The wing formation mechanism is not a settled matter and recently Lee (2000) proposed that Raman scattering of Ly$eta$ by neutral hydrogen is responsible for the broad H$alpha$ wings. In this model, it is predicted that. the Hex wings will be polarized depending on the geometric and kinematic distribution of the scatterers relative to the UV emission region. In this paper, we investigate the polarization of Hex wings in symbiotic stars. Noting that many symbiotic stars possess bipolar nebular morphology, we assume that the distribution of neutral scatterers follows the similar pattern with a receding velocity of several tens of km $s^{-1}$ that mimics the expansion of the neutral envelope of the nebula. It is found that the red wing is more strongly polarized than the blue and main part and that the polarization direction is along the equatorial plane. We obtain a typical degree of polarization $~10$ percent, however, it varies depending on the detailed distribution of H I scatterers We conclude that spectropolarimetry will provide very important information on the origin of the Hex wings.