There is no process that “gives” protons and other charged particles charge. They have charge, regardless of being protons, electrons or neutrons. It’s one of their defining properties. And because charge is (as far as we know) absolutely conserved, there is no process that can give a particle charge or take it away.
Protons, in the modern Standard Model of particle physics, are hadrons, and like neutrons, the other nucleon (particles present in atomic nuclei), are composed of three quarks. Although protons were originally are seen as elementary particles, they are now known to be made of three valence quarks: two up quarks of charge +2/3e and one down quark of charge –1/3e.
However, the rest masses of quarks contribute only about 1% of a proton's mass. The remainder of a proton's mass is due to quantum chromodynamics binding energy, including the quarks' kinetic energy and the energy of the gluon fields that bind the quarks together. Because protons are not elementary particles, they have a physical size, though not a definite one. A proton's root mean square charge radius is about 0.84–0.87 fm or 0.84×10−15 to 0.87×10−15 m.