We present a combined experimental and theoretical investigation of shallow two-dimensional acceptor states in the presence of an external magnetic field for center-doped GaAs/AlxGa1-xAs quantum wells (QW's). The calculated 1S3/2(GAMMA6)-2S3/2(GAMMA6) transition energies of the acceptor state are in excellent agreement with our resonant Raman-scattering data. The g factors obtained from our calculations for varying well width of QW's are also in good agreement with available experimental data. These results confirm the value of the Luttinger parameter kappa = 1.2+/-0.05 for bulk GaAs.