  We analyze the electrostatic self-energy of a point like electrically charged
particle induced by a cosmic string in the context of gravity's rainbow, as
well the electrostatic self-force on this particle. The possibility of the
solution associated with a charged particle to be altered by modifications in
dispersion relations of the space-time is discussed. We show that the
self-energy depends on the rainbow functions and that this quantity can either
increase or decrease depending on the rainbow function chosen, as compared with
analogous result in the framework of general relativity. With respect to the
self-force, its dependence with the rainbow functions is also pointed out
