  We investigate two flavor QCD in presence of CP-odd electromagnetic
background fields and determine, by means of lattice QCD simulations, the
induced effective theta term to the first order in the scalar product of E and
B. We employ a rooted staggered discretization and study lattice spacings down
to 0.1 fm and Goldstone pion masses around 480 MeV. In order to deal with a
positive measure, we consider purely imaginary electric fields and real
magnetic fields, then exploiting analytic continuation. Our results are
relevant to a description of the effective pseudoscalar QED-QCD interactions.
