The "Rust" star and producer is lawyering up with Aaron S. Dyer of Pillsbury Winthrop Shaw Pittman ... according to multiple reports.

Dyer, who spent almost seven years as a federal prosecutor in the U.S. Attorney’s Office in Los Angeles, will reportedly rep Alec plus Rust Movie Productions and the other production companies involved in the western.

As you know ... Alec pulled the trigger in the fatal shooting on set last month that killed cinematographer Halyna Hutchins and injured director Joel Souza.

The revolver was loaded with at least one live round ... though assistant director Dave Halls announced it was a "cold" gun -- meaning no live ammo -- before handing it over to Alec inside a church where they were practicing for a scene.

TMZ broke the story ... the key gaffer on "Rust" is already taking legal action against Alec, Halls and armorer Hannah Gutierrez-Reed ... Serge Svetnoy is suing over the shooting, claiming the defendants' alleged negligence caused him severe emotional distress.

Remember ... Svetnoy claims the deadly bullet nearly hit him too, and says he was one of the first people who tended to Halyna while she was bleeding from her gunshot wound, trying to comfort her and keep her conscious.

Alec is also named in another suit, filed in Los Angeles Superior Court by script supervisor Mamie Mitchell, who claims she suffered emotional and physical injuries when AB shot Halyna.