We report direction dependent magnetization measurements in La_2-xSr_xCuO₄ single crystals. The crystals were grown using traveling solvent floating zone method and were cut into rectangular needle-like shapes with the ”c” direction parallel or perpendicular to the needle symmetry axis. The magnetic anisotropies were studied in details near the critical temperatures using a SQDUID magnetometer. The measurements were done at magnetic fields H<1Oe which is lower than the critical field H_c1 at T->T_c. A difference in T_c of 0.65 K was observed between parallel and perpendicular direction of the optimally doped samples (x=0.15). Higher anisotropy of 2.9 K was observed in under doped samples (x=0.08). We confirmed that the effect is not caused by sample inhomogeneity, needle dimensions, cooling rates, or misalignment. Our results indicate that there is a temperature region where La_2-xSr_xCuO₄ behaves as a two dimensional superconductor.