Tokamaks are toroidal devices to create and confine high-temperature plasmas, and are presently at the forefront of nuclear fusion research. Many parameters in a tokamak are feedback controlled, but some quantities that are either difficult to measure or difficult to control are still controlled by trial-and-error adjustments of feedforward signals. For example, the current density profile plays an essential role in the confinement and stability properties of a tokamak plasma but only few demonstrations exist of feedback control, partly due to the unavailability of the measured variables in real-time on many tokamaks. The aim of this paper it to enhance the control of the current density profile by using batch-to-batch control. An iterative learning controller (ILC) is designed for the current density profile control problem. A simulation study for the future ITER tokamak is shown in which ILC is used to obtain a desired current density profile at the end of the plasma ramp-up phase. Experimental application of ILC to plasma discharges in the TCV tokamak is presented, where the time trajectory of the plasma internal inductance, a scalar measure of the current density profile width, is controlled by varying the total plasma current. Both demonstrate the feasibility of the proposed approach and encourage more extensive use of ILC in tokamak experiments.