In a parallel RC circuit, the supply current "lags" the applied voltage. This is due to the nature of the components involved, resistors (R) and capacitors (C). In an RC circuit, the overall current is the vector sum of the currents through the resistor (in-phase with the voltage) and the capacitor (which leads the voltage by 90 degrees due to its reactance). However, since we are analyzing the overall supply current, we consider the capacitive behavior primarily.
In a purely capacitive circuit, the current leads the voltage by 90 degrees, but in parallel RC circuits, because of the resistive component, the resultant phase angle makes the supply current lag behind the applied voltage.
Therefore, the current lags in phase as a combined effect of these components' behavior.