The core toroidal plasma intrinsic rotation has been studied by experiments and simulations in the Joint Texas Experimental Tokamak (J-TEXT). The direction of core intrinsic rotation in the J-TEXT plasma is counter-current. As the plasma density ramps up, the rotation velocity increases in the counter-current direction. By comparing four different electron densities, linear local gyrokinetic simulations have been performed by the Gyrokinetic Electromagnetic Numerical Experiment code for the first time on J-TEXT. It is found that the most dominant turbulence is the ion temperature gradient at
is the minor radius of the plasma and this is unchanged during the plasma density ramp up. By scanning the radial wave vectors, it is found that the residual stress term reverses from negative to positive when the plasma density exceeds a certain threshold. The pinch term is larger than the residual stress term at all four electron densities, which means that the pinch term is always dominant in the core of a J-TEXT plasma.