I don’t think so. Cargo used to support simpler integration (you could launch make from Cargo.toml) and that has been removed.
Just adding C files doesn’t help you use them from Rust. You need to convert the header files, and even then you end up with a bunch of unsafe functions that aren’t as convenient as native Rust ones.
So the current approach is to make bindings as a *-sys crate that enables easy linking with the C library, and then create a higher-level safe Rust wrapper for it.