  Recently two fundamental topological properties of a magnetic vortex at the
interface of a superconductor (SC) and a strong topological insulator (TI) have
been established: the vortex carries both a Majorana zero-mode relevant for
topological quantum computation and, for a time-reversal invariant TI, a charge
of $e/4$. This fractional charge is caused by the axion term in the
electromagnetic Lagrangian of the TI. Here we determine the angular momentum
$J$ of the vortices, which in turn determines their mutual statistics. Solving
the axion-London electrodynamic equations including screening in both SC and
TI, we find that the elementary quantum of angular momentum of the vortex is
$-n^2\hbar/8$, where $n$ is the flux quantum of the vortex line. Exchanging two
elementary fluxes thus changes the phase of the wavefunction by $-\pi/4$.
