Detailed magnetic-field splitting of the two rotator states designated as (Γ6+Γ8, J=5/2) and (Γ7, J=1/2) associated with donor bound excitons in high-purity epitaxial GaAs is observed in magnetophotoluminescence spectra. These two states are associated with the light-hole mass and are split by the spin-orbit interaction. The ordering in energy of these two states agrees with that predicted by theory. Also observed are the rotator states in which, after the radiative collapse of the exciton, the donor is left in the excited states. A good agreement between the energies of the excited states of the donor as determined experimentally with those calculated using a variational approach is found. The magnetophotoluminescence spectra at relatively low magnetic fields clearly show the evolution of the excited donor bound exciton states as well as the excited rotator states.