Light beams carrying orbital angular momentum (OAM), such as Laguerre-Gaussian (LG) beams, give rise to the violation of the standard dipolar selection rules during interaction with matter, yielding, in general, an exchange of angular momentum larger than h per absorbed photon. By means of ab initio three-dimensional (3D) numerical simulations, we investigate in detail the interaction of a hydrogen atom with intense Gaussian and LG light pulses. We analyze the dependence of the angular momentum exchange with the polarization, the OAM and the carrier-envelope phase of light, as well as with the relative position between the atom and the light vortex. In addition, a quantum-trajectory approach based on the de Broglie-Bohm formulation of quantum mechanics is used to gain physical insight into the absorption of angular momentum by the hydrogen atom. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.