Pull down tomaka's Docker image:
docker pull tomaka/rustc-emscripten
Start a shell and mount the current directory into it:
docker run -it -v $(pwd):/src --rm tomaka/rustc-emscripten /bin/bash
Your code is now accessible in /src
and can be compiled from there:
cd /src rustc --target wasm32-unknown-emscripten hello.rs