We present the Swift X-ray Cluster Survey (SWXCS) catalog obtained using archival data from the X-ray telescope (XRT) on board the Swift satellite acquired from 2005 to 2012, extending the first release of the SWXCS. The catalog provides positions, soft fluxes, and, when possible, optical counterparts for a flux-limited sample of X-ray group and cluster candidates. We consider the fields with Galactic latitude |b| > 20 degree to avoid high HI column densities. We discard all of the observations targeted at groups or clusters of galaxies, as well as particular extragalactic fields not suitable to search for faint extended sources. We finally select ~3000 useful fields covering a total solid angle of ~400 degree^2. We identify extended source candidates in the soft-band (0.5-2keV) images of these fields using the software EXSdetect, which is specifically calibrated for the XRT data. Extensive simulations are used to evaluate contamination and completeness as a function of the source signal, allowing us to minimize the number of spurious detections and to robustly assess the selection function. Our catalog includes 263 candidate galaxy clusters and groups down to a flux limit of 7E-15 erg/cm^2/s in the soft band, and the logN-logS is in very good agreement with previous deep X-ray surveys. The final list of sources is cross-correlated with published optical, X-ray, and SZ catalogs of clusters. We find that 137 sources have been previously identified as clusters, while 126 are new detections. Currently, we have collected redshift information for 158 sources (60% of the entire sample). Once the optical follow-up and the X-ray spectral analysis of the sources are complete, the SWXCS will provide a large and well-defined catalog of groups and clusters of galaxies to perform statistical studies of cluster properties and tests of cosmological models.