The nuclear-spin optical rotation (NSOR) effect, which has potential applications in correlated nuclear-spin-resonance optical spectroscopy, has been explored earlier experimentally and theoretically in liquid Xe. Calculations of the Xe NSOR constant are very challenging because the result is sensitive to correlations, relativistic effects, and the choice of the basis, with strong cancellation between contributions from lowest and remaining states. The relativistic configuration-interaction many-body theory approach, presented here, is promising since this approach has been successful in predicting various properties of noble-gas atoms, such as energies, oscillator strengths (OSs), Verdet constants, and photoionization cross sections. However, correlations become stronger along the sequence of noble-gas atoms and theoretical accuracy in Xe is not as high as for example in neon and argon. To improve the accuracy of the Xe Verdet and NSOR constants, which are calculated as the explicit sums over the excited states, theoretical values for several lowest levels are replaced with empirical values of energies, OSs, and hyperfine structure constants. We found that Xe Verdet constant is in excellent agreement with accurate measurements. To take into account liquid effects, empirical data for energy shifts were also used to correct the NSOR constant. The resulting Xe NSOR constant is in a good agreement with experiment, although the liquid-state effect is treated quite approximately.