  Stimulated by the recent LHCb observation of a new exotic charged structure
$T^{+}_{cc}$, we propose to use the central diffractive mechanism existing in
the $\gamma{}p\to{}D^{+}\bar{T}^{-}_{cc}\Lambda_c^{+}$ ($\bar{T}_{cc}$ is
antiparticle of $T^{+}_{cc}$) reaction to produce $T^{+}_{cc}$. Our theoretical
approach is based on the chiral unitary theory where the $T^{+}_{cc}$ resonance
is dynamically generated. With the coupling constant of the $T^{+}_{cc}$ to
$DD^{*}$ channel obtained from chiral unitary theory, the total cross sections
of the $\gamma{}p\to{}D^{+}\bar{T}^{-}_{cc}\Lambda_c^{+}$ reaction are
evaluated. Our study indicates that the cross section for
$\gamma{}p\to{}D^{+}\bar{T}^{-}_{cc}\Lambda_c^{+}$ reaction are of the order of
1.0 pb, which is accessible at the proposed EicC~\cite{Anderle:2021wcy} and
US-EIC~\cite{Accardi:2012qut} due to the higher luminosity. If measured in
future experiments, the predicted total cross sections can be used to test the
(molecular) nature of the $T^{+}_{cc}$.
