The adsorption behavior of tin phthalocyanine (SnPc) molecules on rutile TiO_{2}(110) was studied by scanning tunneling microscopy (STM). Low-temperature STM measurements of single molecules reveal the coexistence of two conformations of molecules on the TiO_{2} surface. Density functional theory-based simulations (DFT) indicate that the difference originates from the position of the tin atom protruding from the molecule plane. The irreversible switching of Sn-up molecules into the Sn-down conformation was observed either after sample annealing at 200 °C or as a result of tip-induced manipulation. Room-temperature measurements conducted for a coverage of close to a monolayer showed no tendency for molecular arrangement.