The functionalization of graphene remains an important challenge for numerous applications expected by this fascinating material. To keep advantageous properties of graphene after modification or functionalization of its structure, local approaches are a promising road. A novel technique is reported here that allows precise site-selective fluorination of graphene. The basic idea of this approach consists in the local radicalization of graphene by focused ion beam (FIB) irradiation and simultaneous introduction of XeF2 gas. A systematic series of experiments were carried out to outline the relation between inserted defect creation and the fluorination process. Based on a subsequent X-ray photoelectron spectroscopy (XPS) analysis, a 6-fold increase of the fluorine concentration on graphene under simultaneous irradiation was observed when compared to fluorination under normal conditions. The fluorine atoms are predominately localized at the defects as indicated from scanning tunneling microscopy (STM). The experimental findings are confirmed by density functional theory which predicts a strong increase of the binding energy of fluorine atoms when bound to the defect sites. The developed technique allows for local fluorination of graphene without using resists and has potential to be a general enabler of site-selective functionalization of graphene using a wide range of gases.