Can an electromagnetically induced dipole be explained with photon interactions? An incident electromagnetic wave will cause a dipole moment in the medium it passes through, displacing positive and negative charges in accordance with the EM field. How much of this interaction (if any) can be explained via the particle nature of light, i.e. photons?
 A: One of the main reasons we declare that light (and matter) carry both wave and particle properties is because in some situations, we observed that light behaved as a wave, and in others, we observed that it behaved as a particle. The resolution of this was to declare that it must be something that is both, and hence the wave-particle duality was formulated.
What you are asking is "How can we describe a wavelike property of light using a particle description?". If we could, we would have simply said that light is a particle and done away with the wave description of light.
A: 
An incident electromagnetic wave will cause a dipole moment in the medium it passes through, displacing positive and negative charges in accordance with the EM field. How much of this interaction (if any) can be explained via the particle nature of light, i.e. photons?

This depends on the level of abstraction. At a higher level of abstraction it is said that a changing electric field induces a magnetic field and vice versa. This process is called electric and magnetic induction and was observed empirically. Later the explanations became more detailed. Planck's and Einstein’s works made it clear that EM radiation consists of photons, the quanta of any EM radiation.
An incoming radio wave with its high number of aligned photons induces both an electric and a magnetic field inside the receiver's antenna rod. See the Wikipedia for loop antenna, which in the German language are more generally called Magnetantenne.

Can an electromagnetically induced dipole be explained with photon interactions?

As long as you agree that any EM radiation and in particular radio waves consists of photons, you are right to explain the induction processes from this radiation at the level of photon interactions.
