Does firing a proton beam on water make it acidic?
Yes, the concentration of $\ce{H3O+}$ will increase which will lower the pH value of the water. This is theorie based.

In reality you won't be able to measure the change. The mount of protons you need to significantly change the pH will also effect the charge of the water as you mentioned. The charged water will affect your method of measuring AND the protons will leave the water because of it's positive charge.

To neutralize the water you could add elections, which will cause the protons to form hydrogen gas. Or you could add a negative ion like chloride, which would have been the same as adding $\ce{HCl}$ to the water.