CoRoT, the first space-based transit search, provides ultra-high-precision light curves with continuous time-sampling over periods of up to 5 months. This allows the detection of transiting planets with relatively long periods, and the simultaneous study of the host star's photometric variability. In this Letter, we report the discovery of the transiting giant planet CoRoT-Exo-4b and use the CoRoT light curve to perform a detailed analysis of the transit and determine the stellar rotation period. The CoRoT light curve was pre-processed to remove outliers and correct for orbital residuals and artefacts due to hot pixels on the detector. After removing stellar variability about each transit, the transit light curve was analysed to determine the transit parameters. A discrete autocorrelation function method was used to derive the rotation period of the star from the out-of-transit light curve. We determine the periods of the planetary orbit and star's rotation of 9.20205 ± 0.00037 and 8.87 ± 1.12 days respectively, which is consistent with this being a synchronised system. We also derive the inclination, i = 90.00_-0.085+0.000 in degrees, the ratio of the orbital distance to the stellar radius, a/Rs = 17.36-0.25+0.05, and the planet-to-star radius ratio R_p/R_s=0.1047-0.0022+0.0041. We discuss briefly the coincidence between the orbital period of the planet and the stellar rotation period and its possible implications for the system's migration and star-planet interaction history. The CoRoT space mission, launched on December 27th 2006, has been developed and is operated by CNES, with the contribution of Austria, Belgium, Brazil, ESA, Germany, and Spain. The first CoRoT data will be available to the public in February 2009 from the CoRoT archive: http://idoc-corot.ias.u-psud.fr/ Figures 1, 4 and 5 are only available in electronic form at http://www.aanda.org