The pure rotational spectrum of platinum monocarbonyl, PtCO, has been measured between 6500 and 20000 MHz, using a cavity pulsed jet Fourier transform microwave spectrometer. The molecules were prepared by laser ablation of Pt in the presence of CO contained in the Ar backing gas of the jet. Spectra of nine isotopic species have been measured and have been used to determine the molecular geometry. The centrifugal distortion constants agree well with those calculated from a literature force field. The Pt-195 nuclear spin-rotation constant has been used to estimate the Pt-195 shielding and its span.