We present new radial velocity (RV) measurements of old (horizontal branch) and intermediate-age (red clump) stellar tracers in the Carina dwarf spheroidal. They are based on more than 2200 low-resolution spectra collected with VIMOS at Very Large Telescope (VLT). The targets are faint (20<~V<~21.5mag), but the accuracy at the faintest limit is <=9km/s. These data were complemented with RV measurements either based on spectra collected with FORS2 and FLAMES/GIRAFFE at VLT or available in the literature. We ended up with a sample of 2748 stars and among them, 1389 are candidate Carina stars. We found that the intermediate-age stellar component shows a well-defined rotational pattern around the minor axis. The western and the eastern side of the galaxy differ by +5 and -4km/s when compared with the main RV peak. The old stellar component is characterized by a larger RV dispersion and does not show evidence of the RV pattern. We compared the observed RV distribution with N-body simulations for a former disky dwarf galaxy orbiting a giant Milky Way-like galaxy. We rotated the simulated galaxy by 60{deg} with respect to the major axis, we kept the observer on the orbital plane of the dwarf and extracted a sample of stars similar to the observed one. Observed and predicted V_rot_/{sigma} ratios across the central regions are in remarkable agreement. This evidence indicates that Carina was a disky dwarf galaxy that experienced several strong tidal interactions with the Milky Way. Owing to these interactions, Carina transformed from a disky to a prolate spheroid and the rotational velocity transformed into random motions.