We report on the observation of a terahertz radiation-induced photon drag effect in epitaxially grown nand p-type (Bi1-xSbx)(2)Te-3 three-dimensional topological insulators with different antimony concentrations x varying from 0 to 1. We demonstrate that the excitation with polarized terahertz radiation results in a dc electric photocurrent. While at normal incidence a current arises due to the photogalvanic effect in the surface states, at oblique incidence it is outweighed by the trigonal photon drag effect. The developed microscopic model and theory show that the photon drag photocurrent can be generated in surface states. It arises due to the dynamical momentum alignment by time-and space-dependent radiation electric field and implies the radiation-induced asymmetric scattering in the electron momentum space. We show that the photon drag current may also be generated in the bulk. Both surface states and bulk photon drag currents behave identically upon variation of such macroscopic parameters as radiation polarization and photocurrent direction with respect to the radiation propagation. This fact complicates the assignment of the trigonal photon drag effect to a specific electronic system.