The tunneling anisotropic magnetoresistance (TAMR) of single Co atoms adsorbed on a double-layer Fe film on W(110) is observed by scanning tunneling spectroscopy. Without applying an external magnetic field the TAMR is found by comparing spectra of atoms that are adsorbed on the domains and domain walls of the Fe film. The TAMR can be as large as 12% and repeatedly changes sign as a function of bias voltage. First-principles calculations show that the hybridization between Co d states of different orbital symmetries depends on the magnetization direction via spin-orbit coupling. This leads to an anisotropy of the density of states and thus induces a TAMR.