Terahertz absorption spectroscopy plays a key role in physical, chemical and biological systems as a powerful tool to identify molecular species through their rotational spectrum fingerprint. Owing to the sub-nanometer scale of molecules, radiation-matter coupling is typically dominated by dipolar interaction. Here we show that multipolar rotational spectroscopy of molecules in proximity of localized graphene structures can be accessed through the extraordinary enhancement of their multipolar transitions provided by terahertz plasmons. In particular, specializing our calculations to homonuclear diatomic molecules, we demonstrate that a micron-sized graphene ring with a nano-hole at the core combines a strong near-field enhancement and an inherently pronounced field localization enabling the enhancement of the dipole-forbidden terahertz absorption cross-section of H þ 2 by 8 orders of magnitude. Our results shed light on the strong potential offered by nano-structured graphene as a robust and electrically tunable platform for multipolar terahertz absorption spectroscopy at the nanoscale.