Several experiments have revealed the very unusual magnetic properties characterizing ensembles of gold nanoparticles surrounded by organic ligands, including ferromagnetic, paramagnetic, or (large) diamagnetic responses. These experimental observations are at odds with the small diamagnetic response of macroscopic gold samples. We theoretically investigate the possibility that the observed unusual magnetism in capped gold nanoparticles is of orbital origin. Employing semiclassical techniques, we calculate the orbital component to the zero-field susceptibility of individual, as well as ensembles of, metallic nanoparticles. While the result for the orbital response of individual nanoparticles can exceed by orders of magnitude the bulk Landau susceptibility in absolute value, and can be either diamagnetic or paramagnetic depending on nanoparticle size, we show that the magnetic susceptibility of a noninteracting ensemble of nanoparticles with a smooth size distribution is always paramagnetic at low magnetic fields. In particular, we predict that the zero-field susceptibility follows a Curie-type law for small nanoparticle sizes and/or low temperatures. The calculated field-dependent magnetization of an ensemble of diluted nanoparticles is shown to be in good agreement with existing experiments that yielded a large paramagnetic response. The width of the size distribution of the nanoparticles is identified as a key element for the quantitative determination of the orbital response.