WASP-12 is a 2 Gyr old solar type star, hosting WASP-12b, one of the most irradiated transiting planets currently known. We observed WASP-12 in the UV with the Cosmic Origins Spectrograph (COS) on HST. The light curves we obtained in the three covered UV wavelength ranges, all of which contain many photospheric absorption lines, imply effective radii of 2.69±0.24 RJ, 2.18±0.18 RJ, and 2.66±0.22 RJ, suggesting that the planet is surrounded by an absorbing cloud which overfills the Roche lobe. We clearly detected enhanced transit depths at the wavelengths of the MgII h&k resonance lines. Spectropolarimetric analysis of the host star was also performed. We found no global magnetic field, but there were hints of atmospheric pollution, which might be connected to the very unusual activity of the host star.