The influence of resonant magnetic perturbations (RMPs) with a large m/n = 3/1 component on electron density has been studied at J-TEXT tokamak by using externally applied static and rotating RMPs, where m and n are the poloidal and toroidal mode number, respectively. The detailed time evolution of electron density profile, measured by the polarimeter–interferometer, shows that the electron density ne first increases (decreases) inside (around/outside) of the 3/1 rational surface (RS), and it is increased globally later together with enhanced edge recycling. Associated with field penetration, the toroidal rotation around the 3/1 RS is accelerated in the co-Ip direction and the poloidal rotation is changed from the electron to ion diamagnetic drift direction. Spontaneous unlocking-penetration circles occur after field penetration if the RMPs amplitude is not strong enough. For sufficiently strong RMPs, the 2/1 locked mode is also triggered due to mode coupling, and the global density is increased. The field penetration threshold is found to be linearly proportional to neL (line-integrated density) at the 3/1 RS but to (neL)0.73 for ne at the plasma core. In addition, for rotating RMPs with a large 3/1 component, field penetration causes a global increase in electron density.