  We study the Skyrmion of the $SO(2)$ gauged $O(3)$ sigma model in $2+1$
dimensions in the presence of a Skyrme--Chern-Simons (SCS) term, and compare
its properties with the corresponding properties of the Skyrmion in the
presence of the usual Chern-Simons (CS) term. We find that these properties are
qualitatively largely similar in both cases, meaning that the SCS density can
be employed as an alternative to the CS term also in higher dimensions, most
importantly in even dimensions where no CS term is defined, $e.g.,$ in $3+1$
dimensions. The SCS density employed here is defined in terms of the pair of
$SO(2)\times SO(2)$ gauge fields and an auxiliary $O(5)$ Skyrme scalar, which
is contracted to an effective $O(3)$ Skyrme scalar. Technically, this study
maps the methods to be applied in higher dimensional examples.
