A circle graph is a graph in which the adjacency of vertices can be represented as the intersection of chords of a circle. The problem of calculating the chromatic number is known to be NP-complete, even on circle graphs. In this paper, we propose a new integer linear programming formulation for a coloring problem on circle graphs. We also prove that the linear relaxation problem of our formulation finds the fractional chromatic number of a given circle graph. Computational experiments show that a commercial IP solver can find a coloration of a given circle graph quickly under our formulation.