The Rashba effect in Ge/Si$_{0.15}$Ge$_{0.85}$ multiple quantum wells embedded in a p-i-n diode is studied through polarization and time-resolved photoluminescence. In addition to a sizeable redshift arising from the quantum-confined Stark effect, a threefold enhancement of the circular polarization degree of the direct transition is obtained by increasing the pump power over a 2kW/cm$^2$ range. This marked variation reflects an efficient modulation of the spin population and is further supported by dedicated investigations of the indirect gap transition. This study demonstrates a viable strategy to engineer the spin-orbit Hamiltonian through contactless optical excitation and opens the way towards the electro-optical manipulation of spins in quantum devices based on group-IV heterostructures.