  The Witten effect tells that a unit magnetic monopole can bind a half
elementary charge in an axion media. We present an exact solution of a magnetic
monopole in a topological insulator that was proposed to be an axion media
recently. It is found that a magnetic monopole can induce one zero energy state
bound to it and one surface state of zero energy. The two states are quite
robust, but the degeneracy can be removed by external fields. For a finite size
system, the interference of two states may lift the degeneracy, and the
resulting states have one half near the origin and another half around the
surface, which realizes the Witten effect. However, the energy difference
decays exponentially with the size of the system. The exact solution does not
fully support the realization of the Witten effect in a topological insulator.
