Single crystals of tetragonal RCuGa₃ (R=La, Pr, Nd and Gd), with BaNiSn₃ type structure (space group I4 mm), have been grown by high temperature solution growth technique using Ga as flux. Their magnetic properties were determined by heat capacity and the measurement of magnetization and electrical resistivity along [100] and [001] directions. Except LaCuGa₃, the compounds order magnetically. PrCuGa₃ undergoes a ferromagnetic transition with Curie temperature of 4.6 K. NdCuGa₃ shows a bulk magnetic transition at 3.3 K. The data on GdCuGa₃ indicate combined characteristics of spin glass and antiferromagnetic behavior at low temperatures. From the Schottky heat capacity data the crystal electric field level energy spectra have been determined. Further we have performed temperature dependent measurements of electron spin resonance (ESR) on GdCuGa₃ between 11 K and room temperature. The ESR data indicate an enhancement of magnetic fluctuations associated with spin reorientation and both homogeneous and inhomogeneous thermal broadening of the linewidth.