Optically active quantum dots are one of the promising candidates for fundamental building blocks in quantum technology. Many practical applications would comprise of multiple coupled quantum dots, each of which must be individually chargeable. However, the most advanced demonstrations are limited to devices with only a single dot, and individual charging has neither been demonstrated nor proposed for an array of optically active quantum dots. Here we propose and numerically demonstrate a method for controlled charging of multiple quantum dots and charge transport between the dots. We show that our method can be implemented in realistic structures with fidelities greater than 99.9%. The scheme is based on all-optical resonant manipulation of charges in an array of quantum dots formed by a type-II band alignment, such as crystal-phase quantum dots in nanowires. Our work opens new practical avenues for realizations of advanced quantum photonic devices, for instance, solid-state quantum registers with a photonic interface.