In this study, an optical fiber-based magnetically-tuned graphene mechanical resonator (GMR) is demonstrated by integrating superparamagnetic iron oxide nanoparticles on the graphene membrane. The resonance frequency shift is achieved by tuning the tension of the graphene membrane with a magnetic field. A resonance frequency tunability of 23 kHz using a 100 mT magnetic field is achieved. The device provides a new way to tune a GMR with a non-contact force. It could also be used for weak magnetic field detection in the future with further improvements in sensitivity.