Sr2IrO4 has the K2NiF4 structure and its Ir4+ ion (5d(5)) is in a low spin configuration t(2g)(5) with S=1/2. In this paper, we report results of our study on single-crystal Sr2IrO4. Magnetic susceptibility and isothermal magnetization display weak ferromagnetism below 240 K with an easy axis along the a axis and a spin reorientation transition in low magnetic fields. Both the effective paramagnetic moment mu(eff) (=0.5 mu(B)) and the saturation moment mu(s)(=0.14 mu(B)) are found to be quite small, but the ratio of mu(eff)/mu(s) (=3.5) qualitatively fits the Rhodes-Wohlfarth plot. Resistivity, rho(T), along two principal crystallographic directions is strongly anisotropic and shows a metallic behavior below 120 K. Sr2IrO4 exhibits strikingly nonlinear conductivity, i.e., a current-controlled negative differential resistivity for 2 less than or equal to T < 300 K. The origin of the nonohmic behavior may be associated with charge-density-wave depinning. Unlike other systems such as ruthenates Sr2IrO4 appears to show no correlation between conductivity and magnetism.