Context: CoRoT is a pioneering space mission devoted to the analysis of stellar variability and the photometric detection of extrasolar planets. Aims: We present the list of planetary transit candidates detected in the first field observed by CoRoT, IRa01, the initial run toward the Galactic anticenter, which lasted for 60 days. Methods: We analysed 3898 sources in the coloured bands and 5974 in the monochromatic band. Instrumental noise and stellar variability were taken into account using detrending tools before applying various transit search algorithms. Results: Fifty sources were classified as planetary transit candidates and the most reliable 40 detections were declared targets for follow-up ground-based observations. Two of these targets have so far been confirmed as planets, CoRoT-1b and CoRoT-4b, for which a complete characterization and specific studies were performed. The CoRoT space mission, launched on December 27th 2006, has been developed and is operated by CNES, with contributions from Austria, Belgium, Brazil, ESA, Germany, and Spain. Four French laboratories associated with the CNRS (LESIA, LAM, IAS ,OMP) collaborate with CNES on the satellite development. First CoRoT data are available to the public from the CoRoT archive: http://idoc-corot.ias.u-psud.fr.