Molecular rotors with a fixed off-center rotation axis have been observed for single tetra-tert-butyl zinc phthalocyanine molecules on an Au(111) surface by a scanning tunneling microscope at LN2 temperature. Experiments and first-principles calculations reveal that we introduce gold adatoms at the surface as the stable contact of the molecule to the surface. An off-center rotation axis is formed by a chemical bonding between a nitrogen atom of the molecule and a gold adatom at the surface, which gives them a well-defined contact while the molecules can have rotation-favorable configurations. Furthermore, these single-molecule rotors self-assemble into large scale ordered arrays on Au(111) surfaces. A fixed rotation axis off center is an important step towards the eventual fabrication of molecular motors or generators.