We study the isotropic six-vertex model on \mathbb{Z}^2 with spectral parameter \Delta\in[-1,-1/2], that is, with weights \mathbf{a}=\mathbf{b}=1 and \mathbf{c}\in[\sqrt{3},2]. We show that the associated height function converges, in the scaling limit, to a properly scaled full-plane Gaussian free field. The result extends to anisotropic weights \mathbf{a}\neq\mathbf{b} upon using a suitable embedding of the lattice.
