The petition, which has 289,005 signatures at the time of writing, is titled: "We want Johnny Depp back as Captain Jack Sparrow."
A description explains: "He has been playing this role since 2003 when we first saw him arriving at the Port Royal in his boat with that epic background music playing.
"But can you imagine someone else portraying this instead of him? Or no Jack Sparrow at all?
"Even if it means nothing to you but please, sign this petition for the ones who REALLY want Johnny Depp as their Captain of the Black Pearl!" it pleads.
"They have to bring him back to rule the seas again or we will never watch any Pirates of the Caribbean movie without our Captain."
Some of the hundreds of thousands of people who have signed the petition have also commented to say why it's a cause they believe in, with one arguing that Jack Sparrow simply 'is' Pirates of the Caribbean, adding: "The entire franchise wouldn't be the same without his character!"
Someone else wrote: "Johnny Depp is the only person who can and does bring Captain Jack Sparrow to life. He is a genius who knows what to do with a character."
Disney production chief Sean Bailey confirmed in 2018 that Depp was no longer a part of the franchise's future.
He told The Hollywood Reporter: "We want to bring in a new energy and vitality.
"I love the [Pirates] movies, but part of the reason [writers] Paul [Wernick] and Rhett [Reese] are so interesting is that we want to give it a kick in the pants. And that's what I've tasked them with."
At the time, there was also speculation that Disney may have dropped Depp in relation to his personal life.
The Washington Post reported that Disney is said to have ditched the actor four days after Amber Heard's 2018 opinion piece, in which she claimed - without naming anyone - that she had been a victim of domestic abuse.
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