We study the impact of unparticle physics to the chromomagnetic dipole moment (CMDM) of the top quark. We compute the effect induced by unparticle operators of scalar and vector nature coupled to fermions on the CMDM. We find that this dipole moment is sensitive to the scale dimensions $d_u$ of the unparticle and the new couplings of the respective effective operators. Using the bounds imposed on the CMDM by low-energy precision and Tevatron measurements we derive indirect limits on the unparticle parameter space. In particular, we find that the scalar-unparticle operator contribution fulfills both constraints for most of the unparticle parameter space, while the low-energy precision bound on the CMDM excludes a vector-unparticle contribution for low values of respective scale dimension $d_u$.