  Gauge field is essential for exploring novel phenomena in modern physics.
However, it has not been realized in the recent breakthrough experiment about
two-leg superconducting circuits with transmon qubits [Phys. Rev. Lett. 123,
050502 (2019)]. Here we present an experimentally-feasible method to achieve
the synthetic gauge field by introducing ac microwave driving in each qubit. In
particular, the effective magnetic flux per plaquette achieved can be tuned
independently by properly choosing the driving phases. Moreover, the
ground-state chiral currents for the single- and two-qubit excitations are
obtained and the Meissner-vortex phase transition is found. In the Meissner
phase, the ground-state chiral current increases as the magnetic flux
increases, while it decreases in the vortex phase. In addition, the chiral
dynamics that depends crucially on the initial state of the system is also
revealed. Finally, the possible experimental observations of the chiral current
and dynamics are addressed. Therefore, our results provide a new route to
explore novel many-body properties induced by the interplay of gauge field,
two-leg hoppings and interaction of photons on superconducting circuits.
