Mean-square radii of the charge distribution of nucleons are obtained in closed form in terms of meson field operators, by applying a certain transformation to a relativistic one-nucleon theory. They are evaluated by using the pion distribution as given by a modified extended-source theory which takes into account part of the recoil energy of the nucleon. Such a theory derives from the original one-nucleon theory as a result of an expansion in inverse powers of the nucleon mass. The result shows that the radius of the nucleon core, which arises solely from recoil, is much smaller than the one inferred from electron-proton scattering experiments. On the other hand, the recoil correction to the static charge distribution of the pion cloud is negative and so large as almost to cancel the latter.