  This letter presents a generalization of the Drude conductivity for systems
which are exposed to periodic driving. The probe bias is treated perturbatively
by using the Kubo formula, whereas the external driving is included
non-perturbatively using the Floquet theory. Using a new type of four-times
Green's functions disorder is approached diagrammatically, yielding a fully
analytical expression for the Floquet-Drude conductivity. Furthermore, the
Floquet Fermi's golden rule is generalized to $tt'$-Floquet states, connecting
the Floquet-Dyson series with scattering theory for Floquet states. Our
formalism allows for a direct application to numerous systems e.g. graphene or
spin-orbit systems.
