We have calculated the second virial coefficient B(T), including quantum corrections, from a pair potential for hydrogen recently developed from ab initio calculations. Previous comparisons with experimental second virial coefficients used an isotropic simplification of the potential. We compute B(T) for the full anisotropic potential in a semiclassical expansion for temperatures above 100 K and compare the results with experiment. We find that the effect of the anisotropy at the temperatures considered is of similar magnitude to the uncertainty in the best data. Even with this more rigorous calculation, the second virial coefficient predicted by the potential is consistently too positive by an amount somewhat greater than the experimental uncertainty.