We study three-terminal charge transport through individual Fe4 single-molecule magnets. Magnetic anisotropy of the single molecule is directly observed by introducing a spectroscopic technique based on measuring the position of the degeneracy point as a function of gate voltage and applied magnetic field. A nonlinear field-dependence is observed which changes by rotating the sample and is, thus, a direct proof of magnetic anisotropy. The sensitivity of this method allows us to observe small changes in the orientation and magnitude of the anisotropy in different charge states. We find that the easy axes in adjacent states are (almost) collinear.