We propose a possible scheme to realize three-dimensional laser cooling of stored and circulating ion beams in a storage ring. The idea is based on creating a linear synchrobetatron coupling such that the longitudinal laser cooling effect can be extended to transverse degrees of freedom through the coupling. The idea of indirect transverse laser cooling was recently studied, employing a so-called coupling cavity as a source of the forced coupling. In the present paper, we theoretically explore the possibility of using natural dispersion of a ring as an alternative coupling source, setting an ordinary rf cavity at a position with nonzero dispersion. It is found that the effect of the dispersion-induced coupling is essentially equivalent to that of the coupling cavity, and that the coupling can be considerably enhanced under resonance conditions. The cooling rates of longitudinal and transverse modes are evaluated. An approximate formula is derived to estimate an optimum value of dispersion at the cavity location. The validity of the present theoretical predictions is confirmed by tracking simulations that demonstrate effective transverse laser cooling.