An approximate analytical expression for the spin-dependent cross section for Coulomb scattering, valid to order (αZ)4, is developed. The development is based on a modification of the Sommerfeld-Maue wave function. The (αZ)2 and (αZ)3 terms in the resulting cross section are identical with the corresponding terms found by the second Born approximation. The (αZ)4 term is verified by analytically summing the corresponding term in the Mott series. Graphs, comparing the approximate analytical expressions for both the cross section and asymmetry function with exact numerical results, are included.