Tested using Ubuntu MATE 21.10 as a host system. Instructions might require some adjustment for your distro. Assumes Rust is already installed.

Make sure it’s up-to-date:

rustup update

List currently installed toolchains:

rustup show

Default host: x86_64-unknown-linux-gnu
rustup home: /home/jimc/.rustup

stable-x86_64-unknown-linux-gnu (default)
rustc 1.56.0 (09c42c458 2021-10-18)

Your results may differ. Bottom line for me, though, is that I don’t yet have a Windows toolchain installed. I installed a Windows target and toolchain with this:

rustup target add x86_64-pc-windows-gnu
 
rustup toolchain install stable-x86_64-pc-windows-gnu

Create a test project:

mkdir crossplat
 
cd crossplat
 
cargo init --vcs none

A simple main() is generated:

main.rs

fn main() {
    println!("Hello, world!");
}

Make sure it builds and runs:

cargo run

Hello, world!

Install your distribution’s MinGW C compiler:

sudo apt install gcc-mingw-w64-x86-64

Build the project, targeting Windows:

cargo build --target x86_64-pc-windows-gnu

Checking the file type of the generated .exe shows us that it’s a binary for Windows:

file target/x86_64-pc-windows-gnu/debug/crossplat.exe

Result:

target/x86_64-pc-windows-gnu/debug/crossplat.exe: PE32+ executable (console) x86-64, for MS Windows

When you’re ready to deploy to your target system, build the release version with this:

cargo build --target x86_64-pc-windows-gnu --release