In this paper, we develop an immersed Petrov-Galerkin finite element method for solving two-dimensional Stokes interface problems. The proposed method do not require the solution mesh to align with the fluid interface. We utilize the $\text{iso}P_2$-$P_0$ element, which adopts piecewise linear approximation for velocity on fine elements and piecewise constant approximation for pressure on coarse elements. The vector-valued solution map is constructed to approximate the velocity and pressure based on the  jump conditions across the interface. Several numerical experiments demonstrate that the proposed method maintain the optimal convergence rate in the $L_2$-norm and the $H_1$-norm for the velocity and the $L_2$-norm for the pressure.