  In this paper we consider the Dirac oscillator in the context of Doubly
General Relativity or Gravity's Rainbow. In order to obtain the energy levels
of the Dirac oscillator, we solve the Dirac equation in the cosmic string
spacetime modified by gravity's rainbow scenarios described by two rainbow
functions. We then obtain that, as a consequence of the modification of the
cosmic string line element by the two rainbow functions, the energy levels of
the Dirac oscillator are appreciable altered. The results are plotted and
compared with the standard case, without gravity's rainbow effects.
