The high-precision and portable nonlinear magneto-optical rotation (NMOR) atomic magnetometer has significant potential in the direction of magnetic field measurement under a geomagnetic environment. Here, we propose a single-beam NMOR atomic magnetometer with amplitude modulation based on a fiberized electro-optic modulator (EOM) for the first time, to the best of our knowledge, which provides a feasible scheme for the integrated design. A theoretical model of the system response signal as a function of the modulation amplitude is established by a Jones matrix. Based on the theoretical model, the influence mechanism of the modulation amplitude on the system response signal is further analyzed and the optimal modulation parameters can be determined. Finally, a sensitivity of 42.67 fT/Hz1/2 at 50-µT magnetic field is achieved. The proposed scheme is also applicable to other magnetometers under a geomagnetic environment.