Context. One of the most outstanding problems related to numerical models of galaxy formation is the so-called "angular momentum catastrophe", i.e., the inability to theoretically explain the high angular momentum observed in local disk galaxies. Aims. We study the evolution of the angular momentum from z ∼ 0.6 to z = 0 to better understand the mechanisms responsible for the large angular momenta of disk galaxies observed today. This study is based on a complete sample of 32, 0.4 ≤ z ≤ 0.75 galaxies observed with FLAMES/GIRAFFE at the VLT. Their kinematics had been classified as rotating disks (11 galaxies), perturbed rotators (7 galaxies), or complex kinematics (14 galaxies). Methods. We have computed the specific angular momentum of disks ( j disk ) and the dynamical support of rotating disks through the V/σ ratio. To study how angular momentum can be acquired dynamically, we compared the properties of distant and local galaxies, as a function of their kinematical class. Results. We find that distant rotating disks have essentially the same properties ( j disk and R d ) as local disks, while distant galaxies with more complex kinematics have a significantly higher scatter in the j disk -V max and R d -V max planes. On average, distant galaxies show lower values of V/σ than local galaxies, the lowest V/σ values being reached by distant galaxies showing perturbed rotation. This can probably be attributed to heating mechanisms at work in distant disks. Conclusions. We found observational evidence for a non-linear random-walk evolution of the angular momentum in galaxies during the past 8 Gyr. The evolution related to galaxies with complex kinematics can be attributed to mergers, but not to (smooth) gas accretion alone. If galaxies observed at intermediate redshift are related to present-day spirals, then our results match the "spiral rebuilding" scenario proposed by Hammer et al. (2005) quite closely.