We report the direct observation of two mid-gap core d states of differing symmetry for a single Fe atom embedded in GaAs. These states are distinguished by the strength of their hybridization with the surrounding host electronic structure. The midgap state of Fe that does not hybridize via σ bonding is strongly localized to the Fe atom, whereas the other, which does, is extended and comparable in size to other acceptor states. Tight-binding calculations of these midgap states agree with the spatial structure of the measured wave functions and illustrate that such measurements can determine the degree of hybridization via π bonding of impurity d states. These single-dopant midgap states with strong d character, which are intrinsically spin-orbit-entangled, provide an opportunity for probing and manipulating local magnetism and may be of use for high-speed electrical control of single spins.