  Using the quasiclassical concept of Berry curvature we demonstrate that a
Dirac exciton - a pair of Dirac quasiparticles bound by Coulomb interactions -
inevitably possesses an intrinsic angular momentum making the exciton
effectively self-rotating. The model is applied to excitons in two-dimensional
transition metal dichalcogenides, in which the charge carriers are known to be
described by a Dirac-like Hamiltonian. We show that the topological
self-rotation strongly modifies the exciton spectrum and, as a consequence,
resolves the puzzle of the overestimated two-dimensional polarizability
employed to fit earlier spectroscopic measurements.
