The exotic nuclei have attracted extensive attention in nuclear physics recently. The resonant states are thought to play a critical role at the formation of these exotic phenomena. Here, the complex momentum representation (CMR) method for resonances is combined with the relativistic mean field (RMF) theory applicable to deformed system. The RMF-CMR method for deformed exotic nuclei is established. The theoretical formalism and numerical details are presented. Cr-75 is chosen as an example, the energies and widths of single-particle levels and their evolutions to deformation beta(2) are obtained for resonant states together with bound states. The available potential energy curve shows that Cr-75 is a deformed nucleus with beta(2) = 0.333. Wave function of the orbit occupied by the last valence neutron consists mainly of d-wave components. The corresponding density represents a considerably diffuse distribution, which suggests that Cr-75 is a d-wave deformed halo nucleus. The predication is helpful to explore the deformation halos in experiment for the nuclei in the medium mass region.
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