Current regulation of inductive-capacitive-inductive (LCL) grid-connected inverters typically require multiple current sensors to actively damp the filter resonance. Unfortunately, while inverter side current regulation avoids this issue because of its inherent LCL filter damping properties, it does not work well with distorted grids. Furthermore, both strategies require voltage sensors for grid synchronization. This paper proposes a novel current control strategy for LCL grid-connected inverters that requires only inverter side current sensors, with the grid voltage phase and capacitor current estimated from the Proportional Resonant current regulator to achieve self-synchronized indirect regulation of the grid-side current. The effectiveness of the approach has been verified using simulation and matching experimental investigations.