You can always use std::rc::Weak if you need a cyclic data structure with weak references. That covers, I suspect, the majority of the use-cases for these type of structures.

For real, honest-to-god, cyclic data structures — just use unsafe Rust. Again, unsafe Rust isn't "bad". It's just unsafe. More care will be expected of the code to ensure that it exports a safe interface, but nothing in the language stops you from doing it. There's quite literally no loss of expressive power.