We study the rotation rates and electric dipole emission of hydrogenated icosahedral fullerenes under the physical conditions of the dark cloud (DC) LDN 1622. The abundance of fullerenes is estimated by fitting theoretical photoabsorption spectra to the characteristics of the ultraviolet (UV) bump extinction in DCs. The UV bump appears to be well reproduced by a mixture of fullerenes following a size-distribution power law, which gives progressively lower abundances as the radius of the fullerene increases. We infer abundances of the order of 0.2 × 10-6n(H 2) for C60. A significant fraction of these molecules are expected to be hydrogenated. We compute the electric dipole rotational emission from these fullerene hydrides, taking into account rotational excitation and damping processes. The recent detection of anomalous microwave emission (5-60 GHz) in LDN 1622 by Casassus et al. can be explained as the result of electric dipole radiation from hydrogenated fullerenes. The bulk of the emission (10-30 GHz) appears to be associated with 60-80 carbon atom fulleranes with a degree of hydrogenation of C:H ~ 3:1. A small contribution (~10 per cent) of these molecules residing in the surrounding cold neutral medium and/or photodissociation region of the cloud is required to fit the high-frequency tail (40-60 GHz) of the emission.