The absorption energy of atomic hydrogen at rotated graphene bilayers is studied using ab initio methods based on the density functional theory including van der Waals interactions. We find that, due to the surface corrugation induced by the underneath rotated layer and the perturbation of the electronic density of states near the Fermi energy, the atoms with an almost AA stacking are the preferential ones for hydrogen chemisorption. The adsorption energy difference between different atoms can be as large as 80 meV. In addition, we find that, due to the logarithmic van Hove singularities in the electronic density of states at energies close to the Dirac point, the adsorption energy of either electron or hole doped samples is substantially increased. We also find that the adsorption energy increases with the decrease of the rotated angle between the layers. Finally, the large zero point energy of the C-H bond(similar to 0.3 eV) suggests adsorption and desorption of atomic hydrogen and deuterium should behave differently.