We investigate the changes in the infrared response due to charge carriers introduced by electrostatic doping of the correlated insulator vanadium dioxide (VO2) integrated in the architecture of the field effect transistor. Accumulation of holes at the VO2 interface with the gate dielectric leads to an increase in infrared absorption. This phenomenon is observed only in the insulator-to-metal transition regime of VO2 with coexisting metallic and insulating regions. We postulate that doped holes lead to the growth of the metallic islands thereby promoting percolation, an effect that persists upon removal of the applied gate voltage.