Via density functional theory based calculations we show that self-doping of the surface Dirac cones in three-dimensional Bi2X3 (X = Se, Te) topological insulators can be tuned by controlling the sequence of stacking defects in the crystal. Twin boundaries inside the Bi2X3 bulk drive either n- or p-type self-doping of the (0001) topological surface states, depending on the precise orientation of the twin. The surface doping may achieve values up to 300 meV and can be controlled by the number of defects and their relative position with respect to the surface. Its origin relies on the spontaneous polarization generated by the dipole moments associated with the lattice defects. Our findings open the route to the fabrication of Bi2X3 surfaces with tailored surface charge and spin densities in the absence of external electric fields. In addition, in a thin film geometry two-dimensional electron and hole Dirac gases with the same spin-helicity coexist at opposite surfaces.