You can write a patch for the Linux network stack in any language you want. Whether Linus will merge it is a different matter. :P
EDIT: Downvotes eh? Then I suppose I'll state outright what I left implicit: Linux is not inextricably tied to any single language, and it's a strawman to suppose that any attempt to integrate Rust with Linux would first have to reinvent the universe from scratch. Rust has excellent interoperability with C (though, notably, unions are iffy), and it's common to write Rust code that gets called from C with C being none the wiser.
For the record, I don't have enough karma to downvote.
>Linux is not inextricably tied to any single language
It is pretty tightly coupled to GCC, which, as you know, is a C compiler. Some people are working on supporting Clang, but last I heard they haven't succeeded.
It would certainly be interesting to see someone link Linux to Rust code though.
The C ABI is de facto standardized, the compiler in use doesn't matter. Rust code can expose a C ABI and be compiled into a linkable artifact, and that means that C code can use it as though it were an artifact compiled by any C compiler.
"Move to Rust!" is not a productive or helpful suggestion, unless you have an massive army of programmers ready to port Linux to Rust.