  The dark photon is widely predicted in many new physics beyond the Standard
Model. In this work, we propose to utilize the polarized lepton cross section
in neutral current DIS process at the HERA and upcoming Electron-Ion Collider
(EIC) to probe the properties of the dark photon. It shows that we can
constrain the mixing parameter $\epsilon<0.02$ when the dark photon mass
$m_{A_D}<10 ~{\rm GeV}$ at the HERA with polarized lepton beam and this bound
is comparable to the limit from the unpolarized HERA data. With the help of
high integrated luminosity and high electron beam polarization of the EIC, the
upper limit of the $\epsilon$ could be further improved. Depending on the
assumption of the systematic error of the cross section measurements, we obtain
$\epsilon<0.01\sim 0.02$ for the mass region $m_{A_D}<10~{\rm GeV}$ under the
integrated luminosity of $300~{\rm fb}^{-1}$. We also discuss the complementary
roles between the cross section and the single-spin asymmetry measurements in
probing the dark photon.
