Yes, any acid will work to remove rust. It will also dissolve steel too, at a rate commensurate with its acidic strength. (see a pH scale) Molasses will "work", too. (Sulfuric acid).
Most of these suffer from flash rust (once the bare steel is exposed) formed by the reaction of iron and oxygen in the presence of water or air moisture.
From Wiki....
"Rust removal
Phosphoric acid may be used as a "rust converter", by direct application to rusted iron, steel tools, or surfaces. The phosphoric acid converts reddish-brown iron(III) oxide (rust) to black ferric phosphate, FePO4.
After treatment, the black ferric-phosphate coating can be scrubbed off, leaving a fresh metal surface. Multiple applications of phosphoric acid may be required to remove all rust. The black phosphate coating can also be left in place, where it will provide moderate further corrosion resistance. (Such protection is also provided by the superficially similar Parkerizing and blued electrochemical conversion coating processes.)"
Cheers,