  We consider axially symmetric solutions of the U(1) gauged Skyrme model
supplemented with a Callan-Witten (CW) anomaly density term. The main
properties of the solutions are studied, several specific features introduced
by the presence of the CW term being identified. We find that the solitons
possess a nonzero angular momentum proportional to the electric charge, which
in addition to the usual Coulomb part, acquires an extra (topological)
contribution from the CW term. Specifically, it is shown that the slope of
mass/energy $M$ $vs.$ electric charge $Q_e$ and angular momentum $J$ can be
both positive $and$ negative. Furthermore, it is shown that the gauged Skyrmion
persists even when the quartic (Skyrme) kinetic term disappears.
