Only a few hot Jupiters are known to orbit around fast rotating stars. These exoplanets are harder to detect and characterize and may be less common than around slow rotators. Here, we report the discovery of the transiting hot Jupiter XO-6b, which orbits a bright, hot, and fast rotating star: V = 10.25, Teff = 6720 +/- 100 K, v sin i = 48 +/- 3 km/s. We detected the planet from its transits using the XO instruments and conducted a follow-up campaign. Because of the fast stellar rotation, radial velocities taken along the orbit do not yield the planets mass with a high confidence level, but we secure a 3-sigma upper limit Mp < 4.4 MJup. We also obtain high resolution spectroscopic observations of the transit with the SOPHIE spectrograph at the 193-cm telescope of the Observatoire de Haute-Provence and analyze the stellar lines profile by Doppler tomography. The transit is clearly detected in the spectra. The radii measured independently from the tomographic analysis and from the photometric lightcurves are consistent, showing that the object detected by both methods is the same and indeed transits in front of XO-6. We find that XO-6b lies on a prograde and misaligned orbit with a sky-projected obliquity lambda = -20.7 +/- 2.3 deg. The rotation period of the star is shorter than the orbital period of the planet: Prot < 2.12 days, Porb = 3.77 days. Thus, this system stands in a largely unexplored regime of dynamical interactions between close-in giant planets and their host stars.