We use the MusE GAs FLOw and Wind (MEGAFLOW) survey to study the kinematics of extended disc-like structures of cold gas around z=~1 star-forming galaxies. The combination of VLT/MUSE and VLT/UVES observations allows us to connect the kinematics of the gas measured through MgII quasar absorption spectroscopy to the kinematics and orientation of the associated galaxies constrained through integral field spectroscopy. Confirming previous results, we find that the galaxy-absorber pairs of the MEGAFLOW survey follow a strong bimodal distribution, consistent with a picture of MgII absorption being predominantly present in outflow cones and extended disc-like structures. This allows us to select a bona-fide sample of galaxy-absorber pairs probing these discs for impact parameters of 10-70kpc. We test the hypothesis that the disc-like gas is co-rotating with the galaxy discs, and find that for seven out of nine pairs the absorption velocity shares the sign of the disc velocity, disfavouring random orbits. We further show that the data are roughly consistent with inflow velocities and angular momenta predicted by simulations, and that the corresponding mass accretion rates are sufficient to balance the star formation rates.