Dopant ion concentrations in the sides of a symmetric quantum well are known to create a random Rashba-type spin-orbit coupling. Here, we demonstrate that, as a consequence, a finite size spin Hall effect is also present. Our numerical algorithm estimates the result of the Kubo formula for the spin Hall conductivity by using a tight-binding approximation of the Hamiltonian in the framework of a time-dependent Green’s function formalism well suited for very large systems.