Can I swap round a built wall in Rust from soft side to hard side?

You can upgrade the wall to stone or metal and then rotate it, otherwise @kevinthegreat is correct, you will have to demolish the wall and replace it.

EDIT: When upgrading you can rotate a wall when you go from twig -> wood, wood -> stone, stone -> metal and metal -> armoured. Once the wall is fully upgraded or if you skip straight to armoured you cannot rotate it via upgrading.