The Linux Rust installer doesn’t check for a compiler toolchain, but seems to assume that you’ve already got a C linker installed! The best solution is to install the tried-and-true gcc toolchain.
sudo apt install build-essential
If you need to target another architecture, install the appropriate toolchain and target the compilation as follows:
rustc --target=my_target_architecture -C linker=target_toolchain_linker my_rustfile.rs