The synchronization of geodesic acoustic modes (GAMs) and magnetic fluctuations is identified in the edge plasmas of the HL-2A tokamak. Mesoscale electric fluctuations (MSEFs) having components of a dominant GAM, and m/n=6/2 potential fluctuations are found at the same frequency as that of the magnetic fluctuations of m/n=6/2 (m and n are poloidal and toroidal mode numbers, respectively). The temporal evolutions of the MSEFs and the magnetic fluctuations clearly show the frequency entrainment and the phase lock between the GAM and the m/n=6/2 magnetic fluctuations. The results indicate that GAMs and magnetic fluctuations can transfer energy through nonlinear synchronization. Such nonlinear synchronization may also contribute to low-frequency zonal flow formation, reduction of turbulence level, and thus confinement regime transitions.