The selection rules for electron-photon interaction in a two-dimensional electron gas (2DEG) in the presence of the Rashba spin-orbit interaction (RSOI) and quantizing magnetic fields in InGaAs/InAlAs-based spintronic system have been studied based on the semiclassic Boltzmann equation. As a theoretical result, two absorption peaks and abroad band absorption spectrum can be observed for high-mobility samples at relatively high magnetic fields. Similar to the spin-degeneracy system, we find that electronic transitions between the neighboring Landau levels (LLs) within the same spin orientation are the main channels for optical absorption in a spin-split 2DEG. The two absorption peaks originated from the energy spectrum varying with the strength of RSOI and the magnetic fields. And the absorption spectrum can be tuned by the electron density and Rashba parameters. However, due the LLs shifting and mixing induced by the magnetic fields and RSOI, spin-flip transitions were accompanied by the absorption of the photons and the strength of the magnetic-optical absorption peak was relatively weak.