By means of Fabry-Pérot Fourier transform microwave spectroscopy, the rotational spectrum of protonated sulfur dioxide in two distinct isomeric forms, a cis- and a trans-geometry, is reported. The search for both isomers was based on theoretical structures obtained at the CCSD(T)/cc-pwCVQZ level of theory corrected for zero-point vibrational effects. At a similarly high level of theory, the cis-isomer is calculated to be the global minimum on the potential energy surface, but the trans-isomer is predicted to lie only a few kcal/mol higher in energy. A total of seven lines, including a- and b-type transitions, has been observed for both isomers, and precise rotational constants have been derived. Because sulfur dioxide, SO2, is a widespread and very abundant astronomical species, and because it possesses a large proton affinity, HOSO is an excellent candidate for radioastronomical detection.