The nucleon sigma term of the isoscalar and isovector quark chromomagnetic dipole moments are essential inputs for the determination of the CP-odd pion-nucleon couplings induced by quark chromoelectric dipole moments. We demonstrate that the former can be mapped to the third moment of the nucleon twist-three chiral-odd distribution functions e^{q}(x) which are in principle measurable in semi-inclusive deep inelastic scattering processes. We perform a survey on existing model calculations as well as experimental data on e^{u}(x)+e^{d}(x) and derive a predicted range for the isoscalar chromomagnetic dipole moment sigma term.