A systematic program of broadband linear polarimetry, bearing on 55 Ap stars, has been developed during the 4 last years, at the Pic du Midi Observatory. While separate data have been already published, we present in this paper a complete catalogue of our observational material, including more than 400 measurements. We complement these data with another 100 measurements, obtained previously by other authors, so as to get a synthetic view of the phenomenon. Most of the observations have been dedicated to a small number (15) of stars, which show conspicuous changes of the linear polarization, so that it is possible to know accurately the time variation of the Stokes parameters: we expect that these new data will really improve our knowledge of the magnetic configuration, after a proper analysis which is currently being developed. For the other 40 stars, the polarization is either too small, or strongly contaminated by the interstellar polarization, so that broadband polarimetry is not very effective. Anyway, this first systematic investigation on the linear polarization of Ap stars will be a useful starting point for future measurements which should be made with higher spectral resolution. Finally, our measurements have provided new determinations of the rotation period for several stars.