Rotational spectra of five isotopomers of the methylacetylene.SO2 (MA.SO2) van der Waals complex have been observed with a Fourier transform microwave spectrometer. Each species showed two sets of rotational transitions, one associated with the A (m=0) and the other with the E (m=+/-1) methyl group internal rotation states. The rotational transitions of the isotopomers with S O-16(2) and the doubly substituted S O-18(2) also showed inversion splitting ranging from tens of kHz to a few MHz. This splitting was absent in the S O-16 O-18 isotopomers. The spectra of these species have been assigned and fit, yielding rotational constants, which allowed a complete determination of the structure of the complex. The SO2 was found to sit above the carbon-carbon triple bond, with one of the S-O bonds roughly parallel to the symmetry axis of methylacetylene. The centers-of-mass distance between the two monomers was determined to be 3.382(10) Angstrom. The center frequencies of the inversion doublets (or quartets) were used in a fit of both the A and the E transitions; the barrier hindering the internal rotation of the methyl group was determined to be 62.8(5) cm(-1). Based on the dependence of the inversion splitting on the transition dipole direction and isotopic substitution, the inversion motion was identified as an "in plane" wagging of the SO2 relative to methylacetylene. A pure inversion splitting of 3.11 MHz (free from rotation) was extracted from the A-state spectrum of the normal species, from which an inversion barrier height of about 63 cm(-1) was estimated.