  In this paper, we demonstrate the possibility of generating a non-Abelian
Carroll-Field-Jackiw (CFJ) term in the theory of a non-Abelian gauge field
coupled to a spin-3/2 field in the presence of the constant axial vector field.
Applying two regularization schemes, we prove that this term is finite and
ambiguous, particularly vanishing within the 't Hooft-Veltman scheme.
