  We theoretically study the transport signatures of unpaired Floquet Majorana
bound states in the Josephson current of weakly linked, periodically driven
topological superconductors. We obtain the occupation of the Floquet Majorana
modes in the presence of weak coupling to thermal leads analytically, and show
that, similar to static superconductors, the Josephson current involving
Floquet Majorana bound states is also $4\pi$-periodic in the phase difference
across the junction, and also depends linearly on the coupling between
superconductors. Moreover, unlike the static case, the amplitude of the
Josephson current can be tuned by setting the unbiased chemical potential of
the driven superconductors at multiple harmonics of the drive frequency. As a
result, we uncover a Josephson Floquet sum rule for driven superconductors. We
confirm our analytical expressions for Josephson current, the occupation of
Floquet bands, and a perturbative analysis of the quasienergies with
numerically exact results.
