In the recently proposed phenomenon, nuclear spin-induced circular dichroism (NSCD), collective magnetisation of nuclei induces circular dichroism in a light beam passing through a molecular sample. Here we present the first computational predictions of NSCD for fullerenes C₆₀ and C₇₀. We show that the NSCD signal is nucleus-specific, like in NMR spectroscopy. Thus, NSCD may provide a new and promising, high-resolution observable for experimental identification of chemical compounds.