  We investigate the possibility of realizing a disorder-induced topological
Floquet spectrum in two-dimensional periodically-driven systems. Such a state
would be a dynamical realization of the topological Anderson insulator. We
establish that a disorder-induced trivial-to-topological transition indeed
occurs, and characterize it by computing the disorder averaged Bott index,
suitably defined for the time-dependent system. The presence of edge states in
the topological state is confirmed by exact numerical time-evolution of
wavepackets on the edge of the system. We consider the optimal driving regime
for experimentally observing the Floquet-Anderson topological insulator, and
discuss its possible realization in photonic lattices.
