To build a cargo project with musl to crate statically linked binaries, run the following in a fresh directory:

nix flake init -t github:ipetkov/crane#cross-musl

Alternatively, if you have an existing project already, copy and paste the following flake.nix:

{
  description = "Building static binaries with musl";

  inputs = {
    nixpkgs.url = "github:NixOS/nixpkgs/nixpkgs-unstable";

    crane = {
      url = "github:ipetkov/crane";
      inputs.nixpkgs.follows = "nixpkgs";
    };

    flake-utils.url = "github:numtide/flake-utils";

    rust-overlay = {
      url = "github:oxalica/rust-overlay";
      inputs = {
        nixpkgs.follows = "nixpkgs";
        flake-utils.follows = "flake-utils";
      };
    };
  };

  outputs = { nixpkgs, crane, flake-utils, rust-overlay, ... }:
    flake-utils.lib.eachSystem [ "x86_64-linux" ] (system:
      let
        pkgs = import nixpkgs {
          inherit system;
          overlays = [ (import rust-overlay) ];
        };

        rustToolchain = pkgs.rust-bin.stable.latest.default.override {
          targets = [ "x86_64-unknown-linux-musl" ];
        };

        craneLib = (crane.mkLib pkgs).overrideToolchain rustToolchain;

        my-crate = craneLib.buildPackage {
          src = craneLib.cleanCargoSource (craneLib.path ./.);
          strictDeps = true;

          CARGO_BUILD_TARGET = "x86_64-unknown-linux-musl";
          CARGO_BUILD_RUSTFLAGS = "-C target-feature=+crt-static";
        };
      in
      {
        checks = {
          inherit my-crate;
        };

        packages.default = my-crate;
      });
}