  We provide a theory for the tunneling conductance $G(V)$ of Dirac Fermions on
the surface of a topological insulator as measured by a spin-polarized scanning
tunneling microscope tip for low bias voltages $V$. We show that $G(V)$
exhibits an unconventional dependence on the direction of magnetization of the
tip and can be used to measure the magnitude of the local out-of-plane spin
orientation of the Dirac Fermions on the surface. We also demonstrate that if
the in-plane rotational symmetry on the surface of the topological insulator is
broken by an external field, then $G(V)$ acquires a dependence on the azimuthal
angle of the magnetization of the tip. We explain the role of the Dirac
Fermions in this unconventional behavior and suggest experiments to test our
theory.
