We present our $AstroSat$ soft X-ray observations of a compact binary system, AR Sco, and analysis of its X-ray observations with $Chandra$ that were taken only about a week before the $AstroSat$ observations. An analysis of the soft X-ray ($0.3-2.0$ keV) data limits the modulation of the spin, orbital, or beat periods to less than 0.03 counts s$^{-1}$ or $<$10% of the average count rate. The X-ray flux obtained from both observatories is found to be almost identical (within a few percent) in flux, and about 30% lower than reported from the nine months older observations with $XMM-Newton$. A two-temperature thermal plasma model with the same spectral parameters fit $Chandra$ and $AstroSat$ data very well, and requires very little absorption in the line of sight to the source. The low-temperature component has the same temperature ($sim$1 keV) as reported earlier, but the high-temperature component has a lower temperature of 5.0$^{+0.8}_{-0.7}$ keV as compared to 8.0 keV measured earlier, however, the difference is not statistically significant.
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