  We study a non-Abelian Chern-Simons gauge theory in $ 2+ 1$ dimensions with
the inclusion of an anomalous magnetic interaction. For a particular relation
between the Chern-Simons (CS) mass and the anomalous magnetic coupling the
equations for the gauge fields reduce from second- to first order differential
equations of the pure CS type. We derive the Bogomol'nyi-type or self-dual
equations for a $\bphi^2$ scalar potential, when the scalar and topological
masses are equal. The corresponding vortex solutions carry magnetic flux that
is not quantized due to the non-toplogical nature of the solitons. However, as
a consequence of the quantization of the CS term, both the electric charge and
angular momentum are quantized.
