Although Claude Bile gave an excellent answer, valid for all everyday situation and more thereon, I would like to add that at extreme intensities modern theory actually predicts that even in vacuum light can be affected by electromagnetic fields.
Classical electrodynamics obeys Maxwell's equations, which are linear in vacuum, and hence superpostion holds, just like said above. Hence EM-fields cannot interact classically. However, according to Quantum Electrodynamics (QED), there are small non-linear corrections to Maxwell's vacuum equation, allowing EM-fields to interact with each other. That is, QED predicts for instance light-light scattering and light-(E-field) scattering, the later being observed in so called Delbrück scattering (see e.g. G. Jarlskog et al., Phys. Rev. D 8, 3813 (1973)), where light is scattered by the E-field outside a heavy nucleus.
Anyway, again note that those QED-effects only appear at extreme field strengths.