A measurement of the helicity dependence of the total inclusive photoabsorption cross section on the deuteron was carried out at MAMI (Mainz) in the energy range 200<Egamma<800 MeV. The experiment used a 4pi detection system, a circularly polarized tagged photon beam and a frozen-spin target which provided longitudinally polarized deuterons. The contribution to the Gerasimov-Drell-Hearn sum rule for the deuteron determined from the data is 407+/-20(stat)+/-24(syst) mu b for 200<Egamma<800 MeV.