Place the root beer, cinnamon stick and ginger into a small sauce pan and cook over high heat until root beer is reduced by half, about 10 minutes. Lower the heat and add molasses and brown sugar. Cook a few minutes more until thick and syrupy. Keep your eye on the pot and lower the heat if the glaze begins to bubble up the pan too much.
Set the ham on the rack and use a pastry brush to give the ham a layer of the glaze.