We use electron spin resonance in the far infrared to probe the Landau-level spin splitting in symmetric and asymmetric InSb quantum wells. The asymmetric wells exhibit a strong deviation in behavior from the symmetric wells at low magnetic fields with apparent g factors far in excess of the bulk g factor of InSb. These asymmetry-induced shifts in the spin resonance depend on Landau-level index as predicted by the Bychkov-Rashba model. We analyze the shifts to extract values for the Rashba parameter.