  The two-nucleon contributions to the electric dipole moment (EDM) of the
deuteron, induced by the QCD $\theta$-term, are calculated in the framework of
effective field theory up-to-and-including next-to-next-to-leading order. In
particular we find for the difference of the deuteron EDM and the sum of proton
and neutron EDM induced by the QCD $\theta$-term a value of $(-5.4\pm
3.9)\,\bar\theta\times 10^{-4}\, e$ fm. The by far dominant uncertainty comes
from the CP- and isospin-violating $\pi NN$ coupling constant.
