  In the setting of quaternionic Heisenberg group $\mathscr H^{n-1}$, we
characterize the boundedness and compactness of commutator $[b,\mathcal C]$ for
the Cauchy--Szeg\"o operator $\mathcal C$ on the weighted Morrey space
$L_w^{p,\,\kappa}(\mathscr H^{n-1})$ with $p\in(1, \infty)$, $\kappa\in(0, 1)$
and $w\in A_p(\mathscr H^{n-1}).$ More precisely, we prove that $[b,\mathcal
C]$ is bounded on $L_w^{p,\,\kappa}(\mathscr H^{n-1})$ if and only if $b\in
{\rm BMO}(\mathscr H^{n-1})$. And $[b,\mathcal C]$ is compact on
$L_w^{p,\,\kappa}(\mathscr H^{n-1})$ if and only if $b\in {\rm VMO}(\mathscr
H^{n-1})$.
