  We study micromotion in two-dimensional periodically driven systems in which
all bulk Floquet eigenstates are localized by disorder. We show that this
micromotion gives rise to a quantized time-averaged magnetization density when
the system is filled with fermions. Furthermore we find that a quantized
current flows around the boundary of any filled region of finite extent. The
quantization has a topological origin: we relate the time-averaged
magnetization density to the winding number characterizing the new phase
identified in Phys. Rev. X 6, 021013 (2016). We thus establish that the winding
number invariant can be accessed directly in bulk measurements, and propose an
experimental protocol to do so using interferometry in cold atom based
realizations.
