Certain topological aspects of periodically driven quantum systems are unique - similar phenomena do not exist in static systems. One example of such an exotic system is the Anomalous Floquet Anderson Insulator (AFAI), which is a disordered, periodically driven  system where all the bulk states are localized, yet they co-exist with chiral conducting edge states. We show that the unique properties of the AFAI lead to remarkable far-from-equilibrium transport signatures: when connected to leads with a large bias,  the edge states transport a quantized amount of charge per period. We also discuss the possibility of realizing AFAI phases in  more realistic systems, like irradiated graphene.