Metal-oxide-semiconductor field-effect transistors (MOSFETs) on CdTe/HgTe/CdTe heterostructures are fabricated with silicon dioxide gate insulators. In these devices, the density of the quasi two-dimensional electron gas in the HgTe quantum well can be tuned in a wide range. In low magnetic fields we observe beating patterns in the Shubnikov-de Haas oscillations that render possible the determination of the coefficient α of the Rashba term in the Hamiltonian as a function of electron density. This coefficient consistently describes the splittings observed in cyclotron resonance in low magnetic fields.