The convenience of parametrizing the screening charge density induced by a proton in a metal has been stressed by several authors. This parametrization simplifies the description of the charge density and ease its use in different applications. In this work we propose a simple fitting function characterized by a small number of parameters with physical significance. However simple, this function correctly describes charge normalization, asymptotic behavior and cusp condition. Our results compare favorably with previous parametrizations and numerical calculations.