Magnetic field strengths are derived for three H II regions (S117, S119, and S264) from VLA Faraday rotation measures of linearly polarized extragalactic radio sources that lie behind the H II regions. The observed and derived parameters are presented. Two of the extragalactic sources (4C 43.52 and 4C 09.21) are double; in each case, the rotation measures of the two components are identical. Field strengths for S117 (the North American Nebula) and S264 (the H II region surrounding Lambda Orionis) are estimated to be 1 or 2 microgauss; a magnetic strength of 50 microgauss in a molecular cloud of a density of 1000/cu cm is consistent with the existing knowledge of magnetic field strength in molecular clouds. S119 is the brightest part of a thick, ionized shell surrounding the 08 star 68 Cyg, and it has a line-of-sight field of about 20 microgauss. Since the lower limit on the ratio of magnetic to thermal energy density lies between 0.18 and 0.54, it is thought that the magnetic field should have had some effect on the gas dynamics throughout the expansion of the H II region.