We report on the near-infrared polarimetric observations of RCW 120 with the 1.4 m IRSF telescope. The starlight polarization of the background stars reveals for the first time the magnetic field of RCW 120. The global magnetic field of RCW 120 is along the direction of 20{deg}, parallel to the Galactic plane. The field strength on the plane of the sky is 100+/-26uG. The magnetic field around the eastern shell shows evidence of compression by the H II region. The external pressure (turbulent pressure + magnetic pressure) and the gas density of the ambient cloud are minimum along the direction where RCW 120 breaks out, which explains the observed elongation of RCW 120. The dynamical age of RCW 120, depending on the magnetic field strength, is ~1.6Myr for field strength of 100uG, older than the hydrodynamic estimates. In direction perpendicular to the magnetic field, the density contrast of the western shell is greatly reduced by the strong magnetic field. The strong magnetic field in general reduces the efficiency of triggered star formation, in comparison with the hydrodynamic estimates. Triggered star formation via the "collect and collapse" mechanism could occur in the direction along the magnetic field. Core formation efficiency (CFE) is found to be higher in the southern and eastern shells of RCW 120 than in the infrared dark cloud receiving little influence from the H II region, suggesting increase in the CFE related to triggering from ionization feedback.