We study some possible observational signatures of Rn gravity at Galactic scales and how these signatures could be used for constraining this type of f(R) gravity. For that purpose, we performed two-body simulations in the Rn gravity potential and analyzed the obtained trajectories of S2-like stars around the Galactic center, as well as the resulting parameter space of the Rn gravity potential. Here, we discuss the constraints on Rn gravity which can be obtained from the observations of orbits of S2-like stars with the present and next generations of large telescopes. We make comparisons between the theoretical results and observations. Our results show that the most probable value for the parameter rc in the Rn gravity potential in the case of S2-like stars is $\sim${}100\,\,AU, while the universal parameter $\beta${} is close to 0.01. Also, the gravity potential induces the precession of S2-like star orbits in the opposite direction with respect to general relativity; therefore, such a behavior of orbits is qualitatively similar to the behavior of Newtonian orbits with a bulk distribution of matter (including a stellar cluster and dark matter distributions).