In materials lacking inversion symmetry, the spin-orbit coupling enables the direct connection between the electrons spin and its linear momentum, a phenomenon called inverse spin galvanic effect. In magnetic materials, this effect promotes current-driven torques that can be used to control the magnetization direction electrically. In this work, we investigate the current-driven inverse spin galvanic effect in a quantum well consisting in a magnetic material embedded between dissimilar insulators. Assuming the presence of Rashba spin-orbit coupling at the interfaces, we investigate the nature of the non-equilibrium spin density and the influence of the quantum well parameters. We find that the torque is governed by the interplay between the number of states participating to the transport and their spin chirality, the penetration of the wave function into the tunnel barriers, and the strength of the Rashba term.