We calculate the density of states of a donor impurity in a GaAs quantum box under the action of an electric field using effective-mass approximation within a variational scheme. We analyze the behavior of the density of states as a function of the quantum box-size as well as a function of the intensity of the applied electric field, and compare our results with previous reports in quantum wells and quantum well-wires. We expect these results will be of importance in the understanding of experimental absorption spectra related with donor impurities in GaAs quantum boxes under the action of external electric fields.