Single crystals of La_1.8Sr_0.2CuO_4-\delta grown by the travelling solvent floating zone method have been ground to spherical shape for studies of anisotropic supercondcucting properties by SQUID magnetometry. Here we report on magnetization measurements parallel and perpendicular to the c-axis on two of these crystals. At low enough temperatures and fields the spheres are perfectly shielding (susceptibility -1.5 [SI]) and thus magnetically isotropic. The field dependence of the critical temperature, the transition width and the field expulsion well below T_c is qualitatively similar in both samples and is detailed in the paper. The anisotropy of the first critical field also shows similar behavior for the two crystals. Magnetization vs field experiments reveal a large difference in the hysteresis behavior along the two directions and an enhancement of the critical current density through the CuO_2-planes compared to the in-plane current density at higher fields.