We have used high-resolution spectra obtained with the spectrograph FLAMES at the European Southern Observatory Very Large Telescope to determine the kinematical properties and the abundance patterns of 20 blue straggler stars (BSSs) in the globular cluster (GC) M4. We found that ~40% of the measured BSSs are fast rotators (with rotational velocities >50 km s-1). This is the largest frequency of rapidly rotating BSSs ever detected in a GC. In addition, at odds with what has been found in 47 Tucanae, no evidence of carbon and/or oxygen depletion has been revealed in the sample of 11 BSSs for which we were able to measure the abundances. This could be due to either low statistics, or a different BSS formation process acting in M4. Based on observations collected at the ESO-VLT under program 081.D-0356. Also based on observations collected at the ESO-MPI Telescope under program 69.D-0582, and with the NASA/ESA HST, obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS5-26555.