  I consider Compton scattering off the nucleon in the presence of $CP$
violation. I construct the Compton tensor which possesses these features and
consider low energy expansion (LEX) of the corresponding amplitudes. It allows
to separate out the Born contribution which only depends on the static
properties of the nucleon, such as the electric charge, the mass, the magnetic
moment, and the electric dipole moment (EDM). I introduce new structure
constants, the $T$-odd nucleon polarizabilities which parametrize the unknown
non-Born part. These constants describe the response of the $T$-violating
content of the nucleon to the external quasistatic electromagnetic field. As an
estimate, I provide a HBChPT calculation for these new polarizabilities and
discuss the implications for the experiment.
