An edge orientation procedure to generate all acyclic orientations of a graph
The procedure maps each permutation of the vertices to some orientation of the graph whose topological ordering of the vertices is consistent with the permutation.

Every acyclic orientation of the graph induces at least one topological ordering of the vertices.

Every topological ordering of the vertices induces exactly one orientation of the graph (since if two distinct orientations were compatible with the ordering, they would differ in the orientation of at least one edge $(u,v)$ and hence $u$ would come both before and after $v$ in the permutation, which is a contradiction).

So the procedure generates all the acyclic orientations of the graph.