Neutron scattering experiments have been performed to elucidate magnetic properties of the quasicrystal approximant Au70Si17Tb13, consisting of icosahedral spin clusters in a body-centered-cubic lattice. Bulk magnetic measurements performed on the single crystalline sample unambiguously confirm long-range ordering at T C = 11.6 ± 1 K. In contrast to the simple ferromagnetic response in the bulk measurements, single crystal neutron diffraction confirms a formation of intriguing non-collinear and non-coplanar magnetic order. The magnetic moment direction was found to be nearly tangential to the icosahedral cluster surface in the local mirror plane, which is quite similar to that recently found in the antiferromagnetic quasicrystal approximant Au72Al14Tb14. Inelastic neutron scattering on the powdered sample exhibits a very broad peak centered at ℏω ≃ 4 meV. The observed inelastic spectrum was explained by the crystalline-electric-field model taking account of the chemical disorder at the fractional Au/Si sites. The resulting averaged anisotropy axis for the crystalline-electric-field ground state is consistent with the ordered moment direction determined in the magnetic structure analysis, confirming that the non-coplanar magnetic order is stabilized by the local uniaxial anisotropy.