Plastic scintillators are widely used in industry, medicine, and scientific research, including nuclear and particle physics. Although one of their most common applications is in neutron detection, experimental data on their response to low-energy nuclear recoils are scarce. Here, the relative scintillation efficiency for neutron-induced nuclear recoils in a polystyrene-based plastic scintillator (UPS-923A) is presented, exploring recoil energies between 125 and 850 keV. Monte Carlo simulations, incorporating light collection efficiency and energy resolution effects, are used to generate neutron scattering spectra which are matched to observed distributions of scintillation signals to parameterize the energy-dependent quenching factor. At energies above 300 keV the dependence is reasonably described using the semiempirical formulation of Birks and a kB factor of (0.014±0.002) g MeV−1 cm−2 has been determined. Below that energy, the measured quenching factor falls more steeply than predicted by the Birks formalism.