The C ABI is specified in a spec that Linux adopts (eg the x86-psabi), and it is what allows all software using this abi (from assembly to C to Rust) to eg Interface with each other. Linux could write an ABI spec for Rust on its platform today and add a patch to the Rust compiler (or to a C++ comoiler) to adhere to this ABI.
Nobody has done this, and from many povs this is something that does not make much sense doing, but it’s up to the platform to specify how binary software communicates with each other. Linux only specifies this for C, and that’s what Rust software currently does and has to use on Linux.