This paper concerns the behavior of an electron thermalized in supercritical xenon. It is known that the electron can become localized (or self-trapped) in certain ranges of density and temperature. In the case of xenon, localization is enhanced by the strong polarizability. Previous investigations have employed path integral Monte Carlo methods to study the quantum states of the electron and the local properties of the fluid where the electron is treated quantum mechanically and the xenon atoms are treated classically. In this paper we present a reference-interaction-site model (RISM)-polaron calculation for the system of an excess electron in xenon at T=309 K and 248 K. The system is characterized by a Lennard-Jones fluid in which the electron interacts with xenon atoms through a soft potential : a repulsive core with an attractive long range tail. The HNC (hypernetted chain) closure is imposed on the RISM-polaron equation. Significant improvements over the primitive hard sphere model are achieved. The calculation shows that, above the critical density, the electron-solvent radial distribution function g(r) predicted by the RISM-polaron theory is in good agreement with its path integral Monte Carlo counterpart.