Direct measurements of the thermophoretic force on spherical and non-spherical particles have been made using an electrodynamic balance mounted in a vacuum chamber. The non-spherical particles consisted of aggregates of polystyrene latex spheres. By varying the system pressure the force was measured over a wide range of Knudsen numbers ranging from the near-continuum regime to the free-molecule regime. The gases were monoatomic helium and diatomic nitrogen. The data were analyzed and normalized to determine the thermophoretic shape factor that relates the force on a non-spherical particle to that on a sphere of the same volume. The shape factors and the thermophoretic forces are compared with available theories. The measured thermophoretic forces are shown to agree with theories for the Knudsen regime and the free-molecule regime, and the thermophoretic shape factors are shown to be consistent with theories based on the limiting cases of large and small Knudsen numbers.