π-conjugated organic molecules tend to adsorb in a planar configuration on graphene irrespective of their charge state. In contrast, here we demonstrate charging-induced strong structural relaxation of tetrafluorotetracyanoquinodimethane (F4TCNQ) on epitaxial graphene on Ir(111) (G/Ir(111)). The work function modulation over the graphene moiré unit cell causes site-selective charging of F4TCNQ. Upon charging, the molecule anchors to the face-centered cubic sites of the G/Ir(111) moiré through one or two cyano groups. The reaction is reversible and can be triggered on a single molecule by moving it between different adsorption sites. We introduce a model taking into account the trade-off between tilt-induced charging and reduced van der Waals interactions, which provides a general framework for understanding charging-induced structural relaxation on weakly interacting substrates. In addition, we argue that the partial sp3 rehybridization of the underlying graphene and the possible bonding mechanism between the cyano groups and the graphene substrate are also relevant for the complete understanding of the experiments. These results provide insight into molecular charging on graphene, and they are directly relevant for potential device applications where the use of molecules has been suggested for doping and band structure engineering.