In this paper, we consider the stochastic singular integral operators and obtain the BMO estimates. As an application, we consider the fractional Laplacian equation with additive noises \bess du_t(x)=Δ^{\fracα{2}}u_t(x)dt+\sum_{k=1}^\infty\int_{\mathbb{R}^m}g^k(t,x)z\tilde N_k(dz,dt),\ \ \ u_0=0,\ 0\leq t\leq T, \eess where $Δ^{\fracα{2}}=-(-Δ)^{\fracα{2}}$, and $\int_{\mathbb{R}^m}z\tilde N_k(t,dz)=:Y_t^k$ are independent $m$-dimensional pure jump Lévy processes with Lévy measure of $ν^k$. Following the idea of \cite{Kim}, we obtain the $q$-th order BMO quasi-norm of the $\fracα{q_0}$-order derivative of $u$ is controlled by the norm of $g$.