The clip, featuring a narration voiced by Damon from the film Air, was posted on Mr Trump's social media platform Truth Social.
The audio was used over footage of Trump as a young boy and as president.
But the studio said it did not consent to or endorse its usage for Mr Trump's political campaign.
The studio said: "Any use of material from Air by the Trump campaign where approval or consent is required, we do not grant such consent."
