In recent times, the study of iridates has gained major attention and the driving force has been the delicate interplay amongst various energy scales. The local environment of the Ir atom is one of the crucial factors in dictating the properties of such systems and the constant focus has been on Ir in the octahedral or tetrahedral environment. In this work we report the rare occurrence of square planar iridate Cs₂Na₂IrO_4. The structure consists of isolated IrO₄ planes, orthogonally oriented in consecutive layers. Our work involves the  detailed study of electronic and magnetic properties of Cs₂Na₂IrO₄, from first principles calculations. Microscopic magnetic exchange interactions and Wannier function analysis reveals the quasi two dimensional canted AFM ground state, despite the absence of long range structural connectivity which originates because of very weak spin-phonon coupling. The phonon modes analysis further sheds light on the origin of orthogonally placed IrO₄ moieties. Since Ir belongs to the 5d series, it is known to be substantially impacted by SOC. However due to the half-filled situation, the orbital magnetic moment is quenched in this case. Nevertheless we still obtain a large magneto-crystalline anisotropy which could be explained from the second-order perturbation theory. As a guiding tool to experimentalists, we also report preliminary work on muon active sites which is crucial in obtaining the magnetic structure of the system for future studies.