The microwave spectrum of the molecular complex of sulfur dioxide (SO2) with carbon monoxide (CO) has been studied with a pulsed-beam Fourier Transform Microwave Spectrometer (FTMW) from a pair of gas samples of 1 % by volume of SO2 and CO in Ar, and introduced via separate capillary inputs to the flow nozzle. The frequency coverage was about 7 GHz to 16 GHz for various isotopomers. The molecular structure was determined with the aid of spectral studies of isotopically substituted monomers containing 13C, 18O and 34S. The rotational analyses provide the rotational and centrifugal distortion constants for all of the isotopomers analyzed. The structure determination is compared to detailed ab initio structural calculations. The electric dipole moment components along the a- and c-axis were determined from Stark effect measurements.