  We present a dispersive representation of the $\gamma N\rightarrow \pi N$
partial-wave amplitude based on unitarity and analyticity. In this
representation, the right-hand-cut contribution responsible for $\pi N$
final-state-interaction effect are taken into account via an Omn\'es formalism
with elastic $\pi N$ phase shifts as inputs, while the left-hand-cut
contribution is estimated by invoking chiral perturbation theory. Numerical
fits are performed in order to pin down the involved subtraction constants. It
is found that good fit quality can be achieved with only one free parameter and
the experimental data of the multipole amplitude $E_{0}^+$ in the energy region
below the $\Delta(1232)$ are well described. Furthermore, we extend the $\gamma
N\rightarrow \pi N$ partial-wave amplitude to the second Riemann sheet so as to
extract the couplings of the $N^\ast(890)$. The modulus of the residue of the
multipole amplitude $E_{0}^+$ ($S_{11pE}$) is $2.41\rm{mfm\cdot GeV^2}$ and the
partial width of $N^*(890)\to\gamma N$ at the pole is about $0.369\ {\rm MeV}$,
which is almost the same as the one of $N^*(1535)$, indicating that
$N^\ast(890)$ strongly couples to $\pi N$ system.
