Context : The Galactic bulge is a massive , old component of the Milky Way .
It is known to host a bar , and it has recently been demonstrated to have a pronounced boxy/peanut structure in its outer region .
Several independent studies suggest the presence of more than one stellar populations in the bulge , with different origins and a relative fraction changing across the bulge area .

Aims : This is the first of a series of papers presenting the results of the Giraffe Inner Bulge Survey , carried out at the ESO-VLT with the multifibre spectrograph FLAMES .
Spectra of \sim 5000 red clump giants in 24 bulge fields have been obtained at resolution R=6500 , in the infrared Calcium triplet wavelength region at \sim 8500 Å .
They are used to derive radial velocities and metallicities , based on new calibration specifically devised for this project .
Radial velocities for another \sim 1200 bulge red clump giants , obtained from similar archive data , have been added to the sample .
Higher resolution spectra have been obtained for \sim 450 additional stars at latitude b = -3.5 , with the aim of investigating chemical abundance patterns variations with longitude , across the inner bulge .
In total we present here radial velocities for 6392 red clump stars .

Methods : We present here the target selection criteria , observing strategy and the catalogue with radial velocity measurements for all the target stars .

Results : We derive a radial velocity , and velocity dispersion map of the Milky Way bulge , useful to be compared with similar maps of external bulges , and to infer the expected velocities and dispersion at any line of sight .
The K-type giants kinematics is consistent with the cylindrical rotation pattern of M-giants from the BRAVA survey .
Our sample enables to extend this result to latitude b = -2 , closer to the Galactic plane than probed by previous surveys .
Finally , we find strong evidence for a velocity dispersion peak at ( 0 , -1 ) and ( 0 , -2 ) , possibly indicative of a high density peak in the central \sim 250 pc of the bulge .

Conclusions :