The direct perturbation theory of relativistic effects is applied to the Kohn-Sham density functional procedure. The relativistic correction to the total energy is calculated through the leading order. A method for the determination of analytic energy derivatives of the resulting total energy expression is presented, which allows the calculation of the relativistic correction to molecular forces and other first-order properties like e.g. the dipole moment. The method is applied to the diatomic "benchmark" molecules AgH, AuH, and Au-2, and to the transition metal carbonyls Mo(CO)(6) Pd(CO)(4), and W(CO)(6).