We report the infrared transmission measurement on electrically gated twisted bilayer graphene. The optical absorption spectrum clearly manifests the dramatic changes such as the splitting of inter-linear-band absorption step, the shift of inter-van Hove singularity transition peak, and the emergence of very strong intra-valence (intra-conduction) band transition. These anomalous optical behaviors demonstrate consistently the non-rigid band structure modification created by the ion-gel gating through the layer-dependent Coulomb screening. We propose that this screening-driven band modification is an universal phenomenon that persists to other bilayer crystals in general, establishing the electrical gating as a versatile technique to engineer the band structures and to create new types of optical absorptions that can be exploited in electro-optical device application.