We present a universal method to create a tunable, artificial vector gauge potential for neutral particles trapped in an optical lattice. The necessary Peierls phase of the hopping parameters between neighboring lattice sites is generated by applying a suitable periodic inertial force such that the method does not rely on any internal structure of the particles. We experimentally demonstrate the realization of such artificial potentials, which generate ground-state superfluids at arbitrary nonzero quasimomentum. We furthermore investigate possible implementations of this scheme to create tunable magnetic fluxes, going towards model systems for strong-field physics.