  Let $\Omega$ be homogeneous of degree zero, have mean value zero and
integrable on the unit sphere, and $\mu_{\Omega}$ be the higher-dimensional
Marcinkiewicz integral defined by $$\mu_\Omega(f)(x)=
\Big(\int_0^\infty\Big|\int_{|x-y|\leq
t}\frac{\Omega(x-y)}{|x-y|^{n-1}}f(y)dy\Big|^2\frac{dt}{t^3}\Big)^{1/2}. $$ In
this paper, the authors establish a bilinear sparse domination for
$\mu_{\Omega}$ under the assumption $\Omega\in L^{\infty}(S^{n-1})$. As
applications, some quantitative weighted bounds for $\mu_{\Omega}$ are
obtained.
