The orientation switching of a single azobenzene molecule on Au(111) surface excited by tunneling electrons and/or photons has been demonstrated in recent experiments. Here we investigate the rotation behavior of this molecular rotor by first-principles density functional theory (DFT) calculation. The anchor phenyl ring prefers adsorption on top of the fcc hollow site, simulated by a benzene molecule on close packed atomic surface. The adsorption energy for an azobenzene molecule on Au(111) surface is calculated to be about 1.76 eV. The rotational energy profile has been mapped with one of the phenyl rings pivots around the fcc hollow site, illustrating a potential barrier about 50 meV. The results are consistent with experimental observations and valuable for exploring a broad spectrum of molecules on this noble metal surface.