Interesting. I've never seen it proposed as right-associative before. Just FYI, the implementation is as simple as this:
infixr 1 |^
(|^) :: a -> (a -> b) -> b
x |^ f = f x
Then you can write:
3 |^ 2 |^ (^) -- produces 2^3 = 8
It seems very odd to me. I don't know why you'd want to apply the arguments backwards one by one. However, lens and diagrams both provide examples where you want to start with a value and apply functions "forwards" one by one, which is why their corresponding operators are left-associative.