  Let $\Omega\in L^q(S^{n-1})$ with $1<q\le\infty$ be homogeneous of degree
zero and has mean value zero on $S^{n-1}$. In this paper, we will study the
boundedness of homogeneous singular integrals and Marcinkiewicz integrals with
rough kernel on the weighted Morrey spaces $L^{p,\kappa}(w)$ for $q'\le
p<\infty$(or $q'<p<\infty$) and $0<\kappa<1$. We will also prove that the
commutator operators formed by a $BMO(\mathbb R^n)$ function $b(x)$ and these
rough operators are bounded on the weighted Morrey spaces $L^{p,\kappa}(w)$ for
$q'<p<\infty$ and $0<\kappa<1$.
