Recently, Willwacher showed that the Grothendieck-Teichmuller group GRT acts by L-infinity-automorphisms on the Schouten algebra of polyvector fields T-poly(R-d) on affine space R-d. In this article, we prove that a large class of L-infinity-automorphisms on T-poly(R-d), including Willwacher's, can be globalized. That is, given an L-infinity-automorphism of T-poly(R-d) and a general smooth manifold M with the choice of a torsion-free connection, we give an explicit construction of an L-infinity-automorphism of the Schouten algebra T-poly(M) on the manifold M, depending on the chosen connection. The method we use is the Fedosov trick.