  The magnetic critical scattering in Sr$_2$IrO$_4$ has been characterized
using X-ray resonant magnetic scattering (XRMS) both below and above the 3D
antiferromagnetic ordering temperature, T$_{\text{N}}$. The order parameter
critical exponent below T$_{\text{N}}$ is found to be \beta=0.195(4), in the
range of the 2D XYh$_4$ universality class. Over an extended temperature range
above T$_{\text{N}}$, 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 La$_2$CuO$_4$ and
related systems. Our study therefore establishes the importance of XY
anisotropy in the low-energy effective Hamiltonian of Sr$_2$IrO$_4$, the
prototypical spin-orbit Mott insulator.
