  In this work, we have analyzed the $\gamma$-ray data in the energy range 100
MeV to 500 GeV from the \emph{Fermi}-Large Area Telescope (LAT) observations
for the period August 4, 2008 to March 31, 2019. The $\gamma$-ray emission from
AR Scorpii over the last decade is not statistically significant and therefore
2$\sigma$ upper limit on the integral flux above 100 MeV has been estimated. We
reproduce the non-thermal broadband spectral energy distribution of AR Scorpii
using an emission model having two synchrotron components due to the
relativistic electrons in very high magnetic fields. The first component
(Synchrotron-1) broadly describes the emissions at radio to high energy X-rays
through the synchrotron radiation originating from a spherical region of radius
$\sim$ 1.8$\times$10$^{10}$ cm and a magnetic field strength of $\sim$ 10$^3$
Gauss. The second component (Synchrotron-2) which reproduces the X-ray emission
at lower energies and predicts the $\gamma$-ray emission, originates from
another spherical region with radius $\sim$ 1.4$\times$10$^{10}$ cm and a
magnetic field strength of $\sim$ 10$^6$ Gauss. The relativistic electron
populations in both the emission regions are described by a smooth broken power
law energy distribution. The $\gamma$-ray emission predicted by the
Synchrotron-2 model is below the broadband sensitivity of the \emph{Fermi}-LAT
and is also consistent with the 95$\%$ confidence level upper limit on the
integral flux above 100 MeV derived from more than 10 years of observations.
According to our model, the binary system AR Scorpii could be a $\gamma$-ray
source, although its emission level must be below the current detection limit
of the \emph{Fermi}-LAT.
