  The elliptic azimuthal anisotropy coefficient ($v_{2}$) of open-charm hadron
at midrapidity ($|\eta<1|$) was studied in p--Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=$ 8.16 TeV using a multi-phase transport (AMPT) model
included an additional charm quark--antiquark pair production trigger. The
model provides a simultaneously description of the measured $p_{\mathrm{T}}$
spectrum and $v_{2}$ of $D^{0}$ meson, as well as the $v_{2}$ of light flavor
meson $K_{s}^{0}$. We found that the $D^{0}$ and $K_{s}^{0}$ $v_{2}$ are both
significantly affected by different parton scatterings among charm and light
quarks. In addition, the predictions for the $v_{2}$ of other charm hadrons
including $D^{+}$, $D_{s}^{+}$ and $\Lambda_{c}^{+}$ in p--Pb collisions are
given for the first time. The $v_{2}$ of open-charm hadron reasonably follows
the number-of-constituent-quark (NCQ) scaling up to 2.5 GeV, strongly
indicating the importance of partonic degrees of freedom for the collectivity
of heavy flavors in high-multiplicity p--Pb collisions. These findings may hint
the formation of deconfined matter in small collision systems, and provide
referential value for future measurements of azimuthal anisotropy at the LHC
energies.
