We report on our investigations of the electrical resistivity of very thin platinum films, with thickness in the range from 2.6 to 19 nm, formed using a filtered vacuum are plasma deposition method. We find that the resistivity of these films can be well described by a grain-boundary scattering model, especially for thickness less than similar to 5 nm. We also find that the grain size, and consequently the resistivity of the deposited film, is a function of the ion deposition energy, with measured grain size varying from similar to 8 nm for ion deposition energy of 100 eV up to similar to 11 nm at 2.2 keV.