  We study transport properties of a topological insulator nanowire when a
magnetic field is applied along its length. We predict that with strong surface
disorder, a characteristic signature of the band topology is revealed in
Aharonov Bohm (AB) oscillations of the conductance. These oscillations have a
component with anomalous period $\Phi_0=hc/e$, and with conductance maxima at
odd multiples of $\frac12\Phi_0$, i.e. when the AB phase for surface electrons
is $\pi$. This is intimately connected to the band topology and a surface
curvature induced Berry phase, special to topological insulator surfaces. We
discuss similarities and differences from recent experiments on Bi$_2$Se$_3$
nanoribbons, and optimal conditions for observing this effect.
