  Within the QCD light-cone sum rule (LCSR) approach, we investigate the
transition form factors of $D\rightarrow a_0(980)$ up to the twist-3 light-cone
distribution amplitudes (LCDAs) of the scalar meson $a_0(980)$ in the two-quark
picture. Using these form factors, we calculate the differential decay widths
and branching ratios of the $D\rightarrow a_0(980) e^+ \nu_e$ semileptonic
decays. We obtain ${\mathcal B}(D^0\rightarrow a_0^- (980) e^+
\nu_e)=(4.08^{+1.37}_{-1.22})\times 10^{-4}$ and ${\mathcal B}(D^+\rightarrow
a_0^0 (980) e^+ \nu_e)=(5.40^{+1.78}_{-1.59})\times 10^{-4}$. The results are
sensitive to the $a_0(980)$ inner structure. These decays can be searched for
at BESIII experiment, and any experimental observations will be useful to
identify internal quark contents of the $a_0(980)$ meson, which will shed light
on understanding theoretical models.
