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Two-dimensional (2D) rare-earth-based square lattice (SL) quantum magnets provide a pathway to achieve distinctive ground states characterized by unusual excitations. We investigate the magnetic, heat capacity, structural, and electronic properties of a magnetic system Bi₂ErO₄Cl. This compound features a structurally ideal 2D SL composed of Er³⁺rare-earth magnetic ions. The single-phase polycrystalline sample was synthesized using hydrothermal, followed by a vacuum-sealed tube technique. The analysis of heat capacity and magnetic data indicates that the Er³⁺ion adopts aJeff=12state at low temperatures. Fitting the Curie-Weiss (CW) law to the low-temperature magnetic susceptibility data reveals a CW temperature of approximately -2.1 K, suggesting antiferromagnetic (AFM) interactions between the Er³⁺moments. Our first-principles calculations validate a 2D spin model relevant to the titled Er compound. The presence of AFM interaction between the Er³⁺ions is further confirmed using total energy calculations (DFT+<i>U</i>), aligning with the experimental results. The heat capacity measurements reveal the presence of magnetic long-range order below<i>T</i>_N= 0.47 K. The magnetic heat capacity data follows<i>T</i>^1.8power law dependence below<i>T</i>_N.