We report the crystal structure and magnetic properties of a S=3/2 anisotropic triangular lattice compound Na₃Cr(PO₄)₂ employing single-crystal and powder x-ray diffraction, magnetization, heat capacity, and ³¹P nuclear magnetic resonance (NMR) experiments, supported by the band structure calculations. Magnetic susceptibility exhibits a broad maximum around 3.5 K, indicating the presence of a short-range antiferromagnetic order, typical of a low-dimensional spin system. Magnetization and heat capacity manifest an antiferromagnetic long-range ordering at around T_(rm N) ≃ 2.6 K. This was further confirmed by the drastic NMR line broadening and a peak in the nuclear spin-lattice and spin-spin relaxation rates. The isothermal magnetization data exhibit a field-induced spin-flop transition at around μ₀H_(rm SF) ≃ 1.7 T reminiscent of an anisotropic two-dimensional magnet, before saturating above μ₀H_(rm sat) ≃ 4.5 T. The saturation field was further upheld by the field-dependent NMR relaxation measurements at low temperatures. The ³¹P NMR spectral shape confirms the commensurate antiferromagnetic nature of the ordering below T_(rm N). Ab initio calculations reveal a significant deformation of the triangular spin lattice, resulting in triangles with two antiferromagnetic couplings of similar strength and a much weaker coupling along the third side of the triangle.