The refractive index of a y-cut SiO$_2$ crystal surface is reconstructed from polarization dependent soft X-ray reflectometry measurements in the energy range from 45 eV to 620 eV. Due to the anisotropy of the crystal structure in the (100) and (001) directions, we observe a significant deviation of the measured reflectance at the Si-L$_{2,3}$ and O-K absorption edges. The anisotropy in the optical constants reconstructed from these data is also confirmed by ab initio Bethe-Salpeter Equation calculations of the O-K edge. This new experimental dataset expands the existing literature data for quartz optical constants significantly, particularly in the near-edge regions.
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