The magnetic critical scattering in Sr2IrO4 has been characterized using x-ray resonant magnetic scattering (XRMS) both below and above the three-dimensional antiferromagnetic ordering temperature T-N. The order parameter critical exponent below TN is found to be beta = 0.195(4), in the range of the two-dimensional (2D) XYh(4) universality class. Over an extended temperature range above TN, the amplitude and correlation length of the intrinsic critical fluctuations are well described by the 2D Heisenberg model with XY anisotropy. This contrasts with an earlier study of the critical scattering over a more limited range of temperature, which found agreement with the theory of the isotropic 2D Heisenberg quantum antiferromagnet, developed to describe the critical fluctuations of the conventional Mott insulator La2CuO4 and related systems. Our study therefore establishes the importance of XY anisotropy in the low-energy effective Hamiltonian of Sr2IrO4, the prototypical spin-orbit Mott insulator.