We present the results of data analysis of the [CI] ($^{3}P_{1}$-$^{3}P_{0}$) emission from the $rho$ Ophiuchi A photon-dominated region (PDR) obtained in the ALMA ACA stand-alone mode with a spatial resolution of 2.6 (360 au). The [CI] emission shows filamentary structures with a width of $sim$1000 au, which are adjacent to the shell structure seen in the 4.5 $mu$m map. We found that the 4.5 $mu$m emission, C$^0$, and CO are distributed in this order from the excitation star (S1) in a complementary pattern. These results indicate that [CI] is emitted from a thin layer in the PDR generated by the excitation star, as predicted in the plane-parallel PDR model. In addition, extended [CI] emission was also detected, which shows nearly uniform integrated intensity over the entire field-of-view (1.6$times$1.6). The line profile of the extended component is different from that of the above shell component. The column density ratio of C$^0$ to CO in the extended component was $sim$2, which is significantly higher than those of Galactic massive star-forming regions (0.1-0.2). These results suggest that [CI] is emitted also from the extended gas with a density of $n_mathrm{H_2} sim 10^3$ cm$^{-3}$, which is not greatly affected by the excitation star.