K- and L-shell ionization cross sections of gold due to impact of proton and alpha particles have been calculated in the binary encounter approximation incorporating the effects of Coulomb deflection of the projectile, of increase in binding of the target electron, and of polarization and relativity. Relativistic Hartree-Fock-Roothaan (RHFR) momentum distributions for the target electron along with an approximate relativistic correction to the collision dynamics have been used in the present calculations. A comparison with the corresponding calculations using non-relativistic Hartree-Fock-Roothaan wave functions, experimental results and other available calculations is presented.