We report the synthesis and the magnetic properties of single crystalline CeRhAl$_4$Si$_2$ and CeIrAl$_4$Si$_2$ and their non magnetic La-analogs. The single crystals of these quaternary compounds were grown using Al-Si binary eutectic as flux. The anisotropic magnetic properties of the cerium compounds were explored in detail by means of magnetic susceptibility, isothermal magnetization, electrical resistivity, magnetoresistivity and heat capacity measurements. Both CeRhAl$_4$Si$_2$ and CeIrAl$_4$Si$_2$ undergo two antiferromagnetic transitions, first from the paramagnetic to an antiferromagnetic state at $T_{rm N1}$~=~12.6~K and 15.5~K, followed by a second transition at lower temperatures $T_{rm N2}$~=~9.4~K and 13.8~K, respectively. The paramagnetic susceptibility is highly anisotropic and its temperature dependence in the magnetically ordered state suggests the $c$-axis to be the relatively easy axis of magnetization. Concomitantly, isothermal magnetization at 2~K along the $c$-axis shows a sharp spin-flop transition accompanied by a sizeable hysteresis, while it varies nearly linearly with field along the [100] direction up to the highest field 14~T, of our measurement. The electrical resistivity provides evidence of the Kondo interaction in both compounds, inferred from its $-lnT$ behavior in the paramagnetic region. The heat capacity data confirm the bulk nature of the two magnetic transitions in each compound, and further confirm the presence of Kondo interaction by a reduced value of the entropy associated with the magnetic ordering. From the heat capacity data below 1~K, the coefficient of the linear term in the electronic heat capacity, $gamma$, is inferred to be 195.6 and 49.4~mJ/mol K$^2$ in CeRhAl$_4$Si$_2$ and CeIrAl$_4$Si$_2$, respectively classifying these materials as moderate heavy fermion compounds.
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