Can you fake protons with light?

It is commonly said that the electric force is due to the exchange of virtual photons but you need to be very cautious about this statement. The electric force is calculated as if it was due to the exchange of virtual photons, but this is a computational device and virtual photons do not actually exist. There are no virtual photons being sent and received by your proton.

If you shine light at the proton there will indeed be an interaction. With high energy light we get Compton scattering or at lower energy Thomson scattering. But neither of these resemble the electrostatic force. The (real) photons do not produce anything like the electrostatic force because the electrostatic force is not transmitted by photons - it is just calculated that way.