rsigma calculates the resonant disturbing function, R(sigma), for a massless particle in an arbitrary orbit perturbed by a planet in circular orbit. This function defines the strength of the resonance (its semi-amplitude) and the location of the stable equilibrium points (the minima). It depends on the variable sigma called critical angle and on the particle's orbital elements a, e, i and the argument of the perihelion. R(sigma) is numerically calculated and the code is valid for arbitrary eccentricities and inclinations, including retrograde orbits.