It really does depend upon what you mean by 'shift'.
For purely-resistive circuits, the load current is in phase with the supply voltage. For reactive circuits, the load current will lead or lag the supply voltage; for capacitive-resistive circuits, the load current leads, whereas for inductive-resistive circuit, the load current lags.
You can change the angle by which the current leads or lags (the 'phase angle') by changing the amount of resistance or reactance.