The quantum yield of triplets formed by ion-pair recombination in quinone-depleted photosynthetic reaction centers is found to depend on their orientation in a magnetic field. This new effect is expected to be a general property of radical pair reactions in the solid state. For 0 < H < 1,000 G, the quantum yield anisotropy is caused by anisotropic electron dipole-electron dipole or nuclear hyperfine interactions, or both. For high fields it is dominated by the anisotropy of the difference g-tensor in the radical ion-pair. The magnitude and sign of the contribution of each interaction depend not only on the values of the principal components of each anisotropic tensor but also on the geometric relationship of the principal axes of each tensor to the transition dipole moment used to detect the yield. A detailed formalism is presented relating these quantities to the observed yield anisotropy. The expected magnitude of each anisotropic parameter is discussed. It is demonstrated that the field dependence of the yield anisotropy is consistent with these values for certain reaction center geometries.