In fact there used to be a C backend for LLVM, but it was removed in LLVM 3.1 [0]. JuliaHub has resurrected it as a third-party backend [1], though I have no idea if there is any interest in upstreaming the work from either end.

[0]: https://releases.llvm.org/3.1/docs/ReleaseNotes.html

[1]: https://releases.llvm.org/3.1/docs/ReleaseNotes.html