The video emerged after Stokes was arrested following an incident near a Bristol nightclub in September.
“I foolishly attempted to copy the clip after I saw it a few times,” Stokes, 26, tweeted on Wednesday.
“I should never have done this and I am so sorry,” added the Test vice-captain.
“It was absolutely not my intention to offend Harvey, Katie or anybody else. I have written to both Harvey and Katie to say sorry and prior to this offered to meet in person at the end of last month with a view to also getting behind their petition about online bullying. I do hope I can put this right.”
This is the first time Stokes has spoken publicly since he was arrested on suspicion of causing actual bodily harm on a night out that followed England’s victory over West Indies in the third one-day international.
The England and Wales Cricket Board has said Stokes will not travel to Australia on 28 October with the rest of the Ashes squad “at this stage”.