This paper designs a Petrov–Galerkin partially immersed algorithm for Stokes interface problems. We utilize an interface-unfitted uniform triangular mesh. We present an immersed Petrov–Galerkin formulation where the solution spaces satisfy the jump conditions while the test spaces are the standard finite element space. Immersed linear spaces are constructed for velocity, and constant or linear finite element spaces are constructed for pressure, respectively. The standard bubble functions are used to enrich the velocity space to satisfy the inf-sup condition. Numerical examples verify the feasibility of the proposed method.