  From the exact solution of the Dirac-Weyl equation we find unusual currents
j_y running in y-direction parallel to a time-dependent scalar potential
barrier W(x,t) placed upon a monolayer of graphene, even for vanishing momentum
component p_y. In their sine-like dependence on the phase difference of wave
functions, describing left and right moving Dirac fermions, these currents
resemble Josephson currents in superconductors, including the occurance of
Shapiro steps at certain frequencies of potential oscillations. The
Josephson-like currents are calculated for several specific time-dependent
barriers. A novel type of resonance is discovered when, accounting for the
Fermi velocity, temporal and spatial frequencies match.
