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The Galactic bulge is a massive, old component of the Milky Way. It is knownto host a bar, and it has recently been demonstrated to have a pronouncedboxy/peanut structure in its outer region. Several independent studies suggestthe presence of more than one stellar populations in the bulge, with differentorigins and a relative fraction changing across the bulge area. This is thefirst of a series of papers presenting the results of the Giraffe Inner BulgeSurvey, carried out at the ESO-VLT with the multifibre spectrograph FLAMES.Spectra of ~5000 red clump giants in 24 bulge fields have been obtained atresolution R=6500, in the infrared Calcium triplet wavelength region at 8500{\AA}. They are used to derive radial velocities and metallicities, based onnew calibration specifically devised for this project. Radial velocities foranother ~1200 bulge red clump giants, obtained from similar archive data, havebeen added to the sample. Higher resolution spectra have been obtained for 450additional stars at latitude b=-3.5, with the aim of investigating chemicalabundance patterns variations with longitude, across the inner bulge. In totalwe present here radial velocities for 6392 RC stars. We derive a radialvelocity, and velocity dispersion map of the Milky Way bulge, useful to becompared with similar maps of external bulges, and to infer the expectedvelocities and dispersion at any line of sight. The K-type giants kinematics isconsistent with the cylindrical rotation pattern of M-giants from the BRAVAsurvey. Our sample enables to extend this result to latitude b=-2, closer tothe Galactic plane than probed by previous surveys. Finally, we find strongevidence for a velocity dispersion peak at (0,-1) and (0,-2), possiblyindicative of a high density peak in the central 250 pc of the bulge

The GIRAFFE Inner Bulge Survey (GIBS). I. Survey Description and a kinematical map of the Milky Way bulge