The microwave spectrum of the dimethyl ether-sulfur dioxide complex has been observed with a pulsed molecular beam Fourier transform microwave spectrometer. The rotational constants of (CH3)2O.SO2 are A = 4536.747 (12), B = 1865.147 (3), and C = 1457.853 (2) MHz. In addition to the normal isotopic form, the rotational spectra of the (CH3)2O.34SO2, (CH3)2O.S18OO, (CH3)2O.SO-18(2), and 13CH3OCH3.SO2 species were assigned. Only transitions with a- and c-dipole selection rules were observed. Stark effect measurements gave electric dipole components of mu-a = 1.880 (2), mu-c = 0.591 (1) and mu-tot = 1.970 (2) D. The dipole moment and moment of inertia data show that the complex has C(s) symmetry. The two monomers are separated by 3.05 (1) angstrom (R(cm)). The structure of the complex, determined by fitting the moments of inertia, has the planes of the two monomer units in an approximately parallel planes stacked configuration with the oxygen atom of the ether over the sulfur atom of SO2. The O-C bonds eclipse the S-O bonds in SO2.