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Cinematographer Halyna Hutchins died and director Joel Souza was injured in October, when Mr Baldwin was rehearsing drawing a prop gun.
Mr Baldwin, 63, has insisted he "didn't pull the trigger".
The warrant was issued by a Sante Fe court in New Mexico - the state where Rust was being filmed.
It says "there may be evidence on the phone" that could be "material and relevant to this investigation".
Investigators asked to confiscate Mr Baldwin's Apple iPhone that is "believed to be in his possession".
They wanted to look at text messages, emails, web browser history and other information stored on the phone.
It comes two weeks after the star gave his first TV interview about the incident, in which he said he did not pull the trigger, but the gun went off anyway.
"I would never point a gun at anyone and pull a trigger at them. Never," he told George Stephanopoulos of ABC News.
Mr Baldwin said he had been told "it's highly unlikely that I would be charged with anything criminally".
The actor said he is fully co-operating with the police investigation into the shooting.
No criminal charges have been brought against anyone.
A lawsuit against Mr Baldwin alleges that a film script did not require him to fire a gun when he fatally shot Ms Hutchins.
Lawyers handling the suit described the behaviour of Mr Baldwin and the film's producers as "reckless", and accused them of failing to follow safety protocols.
