  We study theoretically the exciton absorption on a ring shreded by a magnetic
flux. For the case when the attraction between electron and hole is
short-ranged we get an exact solution of the problem. We demonstrate that,
despite the electrical neutrality of the exciton, both the spectral position of
the exciton peak in the absorption, and the corresponding oscillator strength
oscillate with magnetic flux with a period $\Phi_0$---the universal flux
quantum. The origin of the effect is the finite probability for electron and
hole, created by a photon at the same point, to tunnel in the opposite
directions and meet each other on the opposite side of the ring.
