We report the discovery of WASP-21b, a new transiting exoplanet discovered by the Wide Angle Search for Planets (WASP) Consortium and established and characterized with the FIES, SOPHIE, CORALIE and HARPS fiber-fed echelle spectrographs. A 4.3-d period, 1.1% transit depth and 3.4-h duration are derived for WASP-21b using SuperWASP-North and high precision photometric observations at the Liverpool Telescope. Simultaneous fitting to the photometric and radial velocity data with a Markov Chain Monte Carlo procedure leads to a planet in the mass regime of Saturn. With a radius of 1.07R_Jup_ and mass of 0.30M_Jup_, WASP-21b has a density close to 0.24{rho}Jup corresponding to the distribution peak at low density of transiting gaseous giant planets. With a host star metallicity [Fe/H] of -0.46, WASP-21b strengthens the correlation between planetary density and host star metallicity for the five known Saturn-like transiting planets. Furthermore there are clear indications that WASP-21b is the first transiting planet belonging to the thick disc.