The rotational spectrum of ScO (X-2 Sigma(+)) has been measured in the gas phase in the frequency range 30-493 GHz using a combination of Fourier transform microwave/millimeter-wave (FTM/mmW) and submillimeter direct absorption methods. This work is the first pure rotational study of this radical. Both the ground vibrational and v=1 states were observed. ScO was created from the reaction of metal vapor, produced either by a laser ablation source or a Broida-type oven, and N2O, in the former case heavily diluted in argon. Extensive hyperfine structure was observed in the FTM/mmW data, although the spin-rotation splitting was found to be small (similar to 3 MHz). In the mm-wave spectra, however, the fine and hyperfine structure was blended together, resulting in broad, single lines for a given transition N + 1 <- N. The data were analyzed in a combined fit using the very accurate hyperfine measurements of Childs and Steimle (1988), employing a Hund's case b Hamiltonian, and an improved set of rotational and centrifugal distortion constants were determined. These measurements improve the accuracy of predicted frequencies for astronomical searches by 14-18 MHz, or 16-20 km/s, in the 1 mm region - a difference of half to a full linewidth for certain interstellar sources. This work also demonstrates the capabilities of the FTM/mmW spectrometer at 61 GHz.