We show that the dynamics of an ultracold bosonic gas loaded into a two-dimensional square optical lattice with anisotropic and time-dependent hopping terms can be described by a Bose-Hubbard model with an effective staggered magnetic field. Besides the uniform superfluid and Mott insulating phases, the zero-temperature phase diagram exhibits a novel kind of superfluid phase, characterized by a quantized staggered rotational flux. This superfluid condenses at finite momentum, a feature known from Fulde-Ferrel-Larkin-Ovchinnikov phases of paired fermions.