  In this paper, we study the effects of a modified theory of gravity - the
rainbow gravity - on the relativistic Bose-Einstein condensate (BEC). We
initially discuss some formal aspects of the model in order to compute the
corrections to the relevant quantities of the condensate. Following, we
evaluate the generating functional from which obtain some thermodynamic
parameters. Then we calculate the corrected critical temperature $T_c$ that
sets the relativistic Bose-Einstein condensate considering the three principal
rainbow functions, finding, in addition, a phenomenological upper bound for the
parameters involved in the model. Finally, we discuss how harder is for the
particles at an arbitrary temperature $T<T_c$ to enter the condensed state
compared to the usual scenario, {\it i.e.}, without rainbow gravity.
