Magnetization measurements on single-crystal cubic SrCuTe2O6 with an applied magnetic field along three inequivalent high symmetry directions , , and  reveal weak magnetic anisotropy. The fits of the magnetic susceptibility to the result from a quantum Monte Carlo simulation on the Heisenberg spin-chain model, where the chain is formed via the dominant third-nearest-neighbor exchange interaction J3, yield the intrachain interaction (J3/kB) between 50.12(7) K for the applied field along  and 52.5(2) K along  with about the same g factor of 2.2. Single-crystal neutron diffraction unveils the transition to the magnetic ordered state as evidenced by the onset of the magnetic Bragg intensity at TN1=5.25(9)K with no anomaly of the second transition at TN2 reported previously. Based on irreducible representation theory and magnetic space group analysis of powder and single-crystal neutron diffraction data, the magnetic structure in the Shubnikov space group P4132, where the Cu2+S=1/2 spins antiferromagnetically align in the direction perpendicular to the spin chain, is proposed. The measured ordered moment of 0.52(6)μB, which represents 48% reduction from the expected value of 1μB, suggests the remaining influence of frustration resulting from the J1 and J2 bonds.