We establish a weighted norm inequality for a class of rough parametric Marcinkiewicz integral operators $mathcal{M}^{ ho}_{Omega}$. As an application of this inequality, we obtain weighted $L^p$ inequalities for a class of parametric Marcinkiewicz integral operators $mathcal{M}^{*, ho}_{Omega,lambda};and;mathcal{M}^{ ho}_{Omega,S}$ related to the Littlewood-Paley $g^*_{lambda}-function$ and the area integral S, respectively.