  Using a current-current correlation function (CF), the photon polarization
tensor is calculated for a rotating hot and dense QCD medium. The spectral
function (SF) and the dilepton rate (DR) are estimated therefrom. Numerical
results show that both SF and DR are enhanced in a rotating medium, especially
in a low invariant mass region. SF and DR are also explored in the consequences
of the interplay among the angular velocity, temperature and chemical
potential. We also estimated the electromagnetic screening by calculating the
Debye mass and it shows a suppression for a rotating QCD medium. The most
interesting observation is the azimuthal anisotropy of the dilepton production,
i.e, the elliptic flow $v_{2}$ of the lepton pair induced by the rotation as an
external field. The competition between the centrifugal effect and the spin
polarization effect due to rotation results in a convex down behaviour of the
elliptic flow as a function of the transverse momentum in a relatively large
magnitude of angular velocity. It is noticed that quark spin polarization
induces a negative $v_2$ in the case of large angular velocity.
