Members of the crowd shouted “CNN sucks” and “Fake News Jim” as people waited for the rally to start in Columbia, South Carolina.
A woman reportedly confronted Mr Acosta – CNN’s chief White House correspondent – near his seat in the press area and then as he stood in front of the cameras.
Reporters at Mr Trump’s rally in support of South Carolina governor Henry McMaster documented the crowd’s taunting of the journalist.
“Sitting next to Acosta is the ... ahem ... ‘best’ seat in the house. Frequent chanting of ‘CNN sucks’, ’Go home, Jim’, after which many have then asked for selfies and autographs,” said Associated Press reporter Meg Kinnard.
But Mr Acosta – who has knocked heads with the Trump administration in the past – was said to have also signed autographs and posed for selfies with Trump supporters at the rally.
According to Buzzfeed News, he signed a hat emblazoned with Mr Trump’s trademark slogan “Make America Great Again”.
When asked why he engaged with the same people who had heckled him, he said: “I think it helps calm them down. If I were to say no, it could make it more venomous.”
Acosta recounted the ordeal of attending the rally on CNN on Monday night – saying it felt totally unprecedented and had left him shocked.
“When I was at this rally tonight, people were coming up to me and saying ‘why are you mean to President Trump, why are mean to Sarah Sanders?’” Acosta told CNN anchor Don Lemon.
“An elderly woman came up to me and said that I needed to get the ‘eff’ out. And then she turned to the crowd and whipped them all into a frenzy and they were saying ‘go home Jim, CNN sucks, fake news,’ and so on. And to me, it’s sort of like, really? This is civility?”
“It’s sort of like being beamed into the twilight zone, Don, covering a political rally where your fellow Americans – you stand for the pledge of allegiance, you do the national anthem – and then they all turn on you and start screaming at you like this. It’s just unlike anything I’ve ever seen before and it’s quite startling.”
The attacks levied at Acosta and CNN come just a week after the crowd at a Trump rally in Duluth in Minnesota chanted “CNN sucks” after the president lambasted the media.
“And I’ve said before if I would have said that to you during the campaign, those very dishonest people back there, the fake news. Very dishonest,” Mr Trump said to boos.
The former property developer, who ordered Acosta out of the Oval Office in January after he asked about the president’s views on immigration, has helped to forge an aggressively hostile attitude to the press among his supporters. He regularly launches into barbed attacks on the media whom he refers to as “fake news”.
Last month, he suggested he could “take away credentials” of media organisations over negative stories about him.
“The Fake News is working overtime.” the US president tweeted. ”Just reported that, despite the tremendous success we are having with the economy & all things else, 91% of the Network News about me is negative (Fake).
“Why do we work so hard in working with the media when it is corrupt? Take away credentials?”
One of Mr Trump’s most brazen attacks on the media came when he posted a video of himself body slamming CNN on Twitter last July.
He appeared to promote violence against the news network by tweeting old footage of himself performing at a 2007 World Wrestling Entertainment professional wrestling match but with his opponent’s face covered with the broadcaster's logo.
The president has reportedly spent time in the White House watching cable TV in his bathrobe and marking up negative news stories with a black sharpie.
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