What color would a proton be if it were visible to the human eye? If a photon hits a proton, would it have a color? What color would it be?
 A: Mie theory and its long-wavelength limit, Rayleigh scattering, says "blue", thanks to the $1/\lambda^4$ term; however, this is not correct. Mie theory is predicated on scattering from a neutral dielectric sphere and is computed (classically) by matching the EM boundary conditions at the surface of the sphere.
The proton is not neutral, nor is it polarizable like a dielectric sphere--so those aforementioned mechanisms are not in effect.
I think the correct mechanism is Compton scattering, so one must extend the Klein-Nishina formula to low energy to answer this hypothetical question. The details are here: https://en.wikipedia.org/wiki/Klein–Nishina_formula 
What we learn qualitatively by looking at the angular distribution with various energies is that forward scattering is independent of frequency, while backwards scattering falls off rapidly with energy.
This means that backlit protons are white, and as the observer changes angle to look at direct reflections, the protons become more and more red--and they are very red when illuminated head-on.
A: Blue.  
The proton is way smaller than a wavelength of visible light.  But blue light has a shorter wavelength than any other visible color, red light is longer wavelength, blue is shorter, other colors in the middle somewhere.  
White light is a mixture of all the colors of light, all the wavelengths in the visible range.  If you illuminate the proton with white light, almost all the white light will just go past the proton, not reflect back, because the proton is so small.  But of the small amount of light that does reflect back, a higher fraction of it will be blue light and a lower fraction of it will be red light.  So the reflection would appear blue.  
This is pretty much the same effect that makes the sky blue.  Tiny particles in the sky don't reflect much of the sun's light going past them, but of the small amount they do reflect, more of it is blue than any other color.  
A: See yourself. This is a photo:

From here.
A: The color of the proton would be the color of the photon you are using. This is assuming the photon scatters off of the proton and goes into your eyes. Our eyes only detect visible light, so we can only see those colors. If the photon you are using does not scatter off of the proton and go back to your eye, then you won't see it at all. Also, I don't believe protons absorb photons, only electrons do. (Correct me if I am wrong physics community). Thus, you can only count on scattering. Then again, visible light's wavelengths, (hundreds of nanometers), are larger than a proton, so it'd be hard to get scatter in the first place. So in the end, I think you won't be able to see it at all if you are using visible light.
A: If your eye could detect protons, which it doesn't, but if it did, your brain would assign it a color. Not red, not blue, not green or any other combination. It would be proton colored. So the answer to the title question is 'proton colored'.
