Biden says, "I see that you are on the job and presidential, as always."
Earlier in the day, Trump had tweeted a parody video making fun of Biden as he pledged to alter behavior that made some women uncomfortable.
Biden's pledge took place in a video in which he said he understood that his touchy-affectionate behavior upset some women and pledged to change his ways. Biden seemed to be seeking to ease some people's discomfort, which has raised questions about whether he could wage an effective presidential campaign.
But the doctored video retweeted by Trump shows images of Biden popping up behind the former vice president, touching and nuzzling him. Trump added the caption "WELCOME BACK JOE!"
Several women have come forward in recent days to complain about Biden making them uncomfortable. More than a dozen have accused Trump of sexually harassing them. Trump has denied the charges.