On-surface fabrication of two-dimensional (2D) metal organic frameworks (MOFs) has been continuously attracting attentions for years. However, the synthesis of 2D MOFs with large-amplitude flexibility was rarely carried out since the bonding configurations in the coordination nodes are typically highly directional. Here we demonstrate that single alkali ions, which are fully isotropic in ionic bonding, can act as pivot joints for constructing tunable 2D MOFs by bonding to dihalogen groups in organic molecules. We take 2,3,6,7,10,11-hexabromotriphenylene, a 3-fold polycyclic molecule with three ortho-dibromo groups, and sodium (Na) atoms as a model system and successfully construct Na-based MOFs on Au(111) surface. The deflection angle of the Na coordination nodes is variable in an unprecedentedly large range between ±36° that allows the construction of multiple 2D MOF architectures. Such a flexible alkali-halogen bonding may provide a unique toolbox for designing and constructing more tunable MOFs by choosing various alkali atoms and halogen moieties.