By considering strict relativistic energy of single particle and using the methods of quantum statistics, the relativistic paramagnetism of a weakly interacting Fermi gas in a weak magnetic filed is studied, and the relativistic most probable paramagnetic susceptibility as well as the average magnetic susceptibility of the system are solved. On the basis, the influences of relativistic effect on the most probable paramagnetic susceptibility of the system are discussed, and the relativistic critical value of particle number is given. It is shown that, comparing with nonrelativistic situation, when $T\gg T_F,$ the relativistic most probable magnetic susceptibility and the relativistic critical value of particle number have not changed. When $T\ll T_F$, the relativistic effects make the system display paramagnetism easily and susceptibility increase, but the relativistic effects also amplified the impact of the interaction on the magnetic susceptibility.