The most massive stars can form via standard disk accretion--despite the radiation pressure generated--due to the fact that the massive accretion disk yields a strong anisotropy in the radiation field, releasing most of the radiation pressure perpendicular to the disk accretion flow. Here, we analyze the self-gravity of the forming circumstellar disk as the potential major driver of the angular momentum transport in the massive disks responsible for the high accretion rates needed for the formation of massive stars. For this purpose, we perform self-gravity radiation hydrodynamic simulations of the collapse of massive pre-stellar cores. The formation and evolution of the resulting circumstellar disk is investigated in (1) axially symmetric simulations using an Delta *a-shear-viscosity prescription and (2) a three-dimensional simulation in which the angular momentum transport is provided self-consistently by developing gravitational torques in the self-gravitating accretion disk. The simulation series of different strengths of the Delta *a viscosity shows that the accretion history of the forming star is mostly independent of the Delta *a-viscosity parameter. The accretion history of the three-dimensional run driven by self-gravity is more time dependent than the viscous disk evolution in axial symmetry. The mean accretion rate, i.e., the stellar mass growth rate, is nearly identical to the Delta *a-viscosity models. We conclude that the development of gravitational torques in self-gravitating disks around forming massive stars provides a self-consistent mechanism to efficiently transport angular momentum to outer disk radii. The formation of the most massive stars can therefore be understood in the standard accretion disk scenario.