Measurements of five pure rotational transitions of a mixed isotopomer of the CO-CO van der Waals dimer with a Fourier transform microwave spectrometer in the frequency range from 3 to 19 GHz are reported. For symmetry reasons, pure rotational transitions in the vibrational ground state are not accessible in the symmetric (CO)-C-12-O-16-(CO)-C-12-O-16 species, and the mixed (CO)-C-12-O-16-(CO)-C-13-O-16 isotopomer was studied instead. The observed lines were identified as belonging to the (CO)-C-12-O-16-(CO)-C-13-O-16 dimer by isotopomeric variation of the sample composition, monitoring of the microwave excitation pulse conditions, and comparison of the measured frequencies with those predicted in a recent infrared study. [M. D. Brookes and A. R. W. McKellar, J. Chem. Phys. (submitted).]