The ability to reproduce the structure of water around the sodium and potassium ions as determined by experiment is a key test of the quality of interaction potentials due to the central importance of these ions in a wide range of important phenomena. Here, we simulate the Na+ and K+ ions in bulk water using the recently developed strongly constrained and appropriately normed (SCAN) functional and compare with experimental X-ray diffraction (XRD) and X-ray adsorption fine structure (EXAFS) measurements to demonstrate that it accurately reproduces important structural details of the hydration structure of the sodium and potassium cations. We demonstrate that it performs substantially better than the generalized gradient approximation (GGA) based dispersion corrected revised Perdew, Burke, and Ernzerhof functional (revPBE-D3) and is even better than the random phase approximation level for potassium. Both of these functionals have been demonstrated to accurately reproduce the structure of bulk water. This improved performance compared with revPBE-D3 is attributed to smaller fluctuations of the mean error of ion-water cluster binding energies utilizing a novel benchmark for testing functionals.