Millimetre Waves (mmWave) systems have the potential of enabling multi-gigabit-per-second communications in future Intelligent Transportation Systems (ITSs). Unfortunately, because of the increased vehicular mobility, they require frequent antenna beam realignments - thus significantly increasing the in-band Beamforming (BF) overhead. In this paper, we propose Smart Motion-prediction Beam Alignment (SAMBA), a MAC-layer algorithm that exploits the information broadcast via DSRC beacons by all vehicles. Based on this information, overhead-free BF is achieved by estimating the position of the vehicle and predicting its motion. Moreover, adapting the beamwidth with respect to the estimated position can further enhance the performance. Our investigation shows that SAMBA outperforms the IEEE 802.11ad BF strategy, increasing the data rate by more than twice for sparse vehicle density while enhancing the network throughput proportionally to the number of vehicles. Furthermore, SAMBA was proven to be more efficient compared to legacy BF algorithm under highly dynamic vehicular environments and hence, a viable solution for future ITS services.