Single-crystal silicon is one of the most promising materials for producing test masses for the new generation of laser interferometers intended for the detection of gravitational waves. We studied the thermally induced depolarization of radiation in single-crystal silicon with [001] orientation at a wavelength of 1940 nm at room temperature. The value of the piezo-optical anisotropy ratio was found to be ξ = -0.63 ± 0.05 for one manufacturer and ξ = 0.62 ± 0.05 for another. The physical reason for the different signs was not established, and the search for this reason will continue. For the single-crystal silicon with the negative piezo-optical anisotropy ratio, the directions of the special orientations [C] and [P] for which thermally induced depolarization and thermal lens astigmatism vanish, respectively, were determined. When ξ is close to -0.5, the special orientations are close to [111], making this orientation preferable to the other traditionally used orientation, [001].