We calculate exactly the vacuum polarization charge density in the field of a subcritical Coulomb impurity, , in graphene. Our analysis is based on the exact electron Green’s function, obtained by using the operator method, and leads to results that are exact in the parameter , where is the “fine-structure constant” of graphene. Taking into account also electron-electron interactions in the Hartree approximation, we solve the problem self-consistently in the subcritical regime, where the impurity has an effective charge , determined by the localized induced charge. We find that an impurity with bare charge remains subcritical, , for any , while impurities with , 3 and higher can become supercritical at certain values of .