We validate the linear dispersion relation (Dirac cone) on the surface of a single Bi2Te3 nanowire via a combination of field-effect and magnetoresistance measurements by which we unambiguously prove the topological insulator nature of the nanowire surface states. Moreover, we show that the experimentally determined carrier concentration, mobility, and cyclotron mass of the surface states are in excellent agreement with relativistic models. Our method provides a facile way to identify topological insulators that too small for angle-resolved photoemission spectroscopy.