We report a measurement of the spin-dependent total cross section ratios delta_sigma_T/sigma_tot and delta_sigma_L/sigma_tot of the pp --> pp pi^0 reaction between 325 MeV and 400 MeV. The experiment was carried out with a polarized internal target in a storage ring. Non-vertical beam polarization was obtained by the use of solenoidal spin rotators. Near threshold, the knowledge of both spin-dependent total cross sections is sufficient to deduce the strength of certain participating partial waves, free of any model.