The magnetic sublevel specific preparation of the \X (1)Sigma(g)(+),v=1,J=1] state of molecular H-2 using stimulated Raman pumping with circularly polarized light to saturate the Q(01)(1) transition is reported. The intensities of S branch rotational Raman scattering signals for the v=0 and v=1 states combined with their depolarization ratios measured as a function of pumping light polarization provide direct evidence of the m(J) selective nature of the pumping process. This Raman method of non-Boltzmann population preparation does not require a permanent dipole moment and is generally applicable to a wide range of systems.