Spectro-polarimeteric observations in the vacuum-ultraviolet (VUV) region are expected to be developed as a new astrophysics diagnostic tool for investigating space plasmas with temperatures of >10(4) K. Precise measurements of the difference in the extraordinary and ordinary refractive indices are required for developing accurate polarimeters, but reliable information on the birefringence in the VUV range is difficult to obtain. We have measured the birefringence of magnesium fluoride (MgF2) with an accuracy of better than ±4×10(-5) around the hydrogen Lyman-α line (121.57 nm). We show that MgF2 can be applied practically as a half-waveplate for the chromospheric Lyman-alpha spectro-polarimeter (CLASP) sounding rocket experiment and that the developed measurement method can be easily applied to other VUV birefringent materials at other wavelengths.