The man, who has not been named, was called a "racial slur" after finishing a shift at the Georgia secretary of state's election warehouse in Cobb County, officials said.
It comes just days after a top Georgia election official warned “someone is going to get killed” if Mr Trump continues with his unsubstantiated claims of ballot irregularities.
Election storage facilities play no role in vote counting. Instead, they supply polling stations with ballot papers, pencils and other items needed to ensure that voting can take place.
After departing the warehouse car park for home, officials said, the worker noticed that his car was being tailed by an unknown member of the public.
In fear of his safety, he decided not to lead the assailant back to his home and headed for a Cobb County police station.
At that point, the person who was following the worker disappeared, Michael Barnes, a supervisor at the warehouse, said.
"It's a shame that people who are just doing their job are being treated in such vile ways," he added. "It made me shiver".
Wednesday's incident is just one in a number of attempts by members of the public to intimidate election workers in Georgia, where president-elect Joe Biden's victory was upheld last month following a recount.
Despite losing by some 13,000 votes, Mr Trump continues to insist that he won the traditionally red state, citing false and unsubstantiated claims of voter fraud.
His legal team is currently contesting 100,000 ballots in the state.
Mr Barnes told WSBTV workers at the warehouse have been receiving abuse since polling day on 3 November, when staff were forced to walk back to their cars in pairs.
People have also been recording workers on shift and posting the images on social media, he said. Workers' car number plates have also been filmed.
"Some of them scream, 'you're going to jail, you're going to jail!'" Mr Barnes added.
Jordan Fuchs, Georgia's Republican deputy secretary of state, said security was being ramped up at the storage facility, to make sure "our team members are safe and that they are protected".
Local police officers have increased patrols in the area and on Thursday escorted some workers home, Mr Barnes said.
The Cobb County incident has emerged just days after one of Georgia's top election officials pleaded with Mr Trump to dial down his rhetoric on the election.
Gabriel Sterling, a Republican who oversaw the implementation of the state’s new voting system, said "someone is going to get killed" if the outgoing president persisted.
Mr Sterling has himself been targeted and recently had to have police protection at his home. "The harassment and potential for violence continue to escalate for elections employees," he said of the Cobb County incident.
But the outgoing commander-in-chief doesn't appear to be listening to the impassioned pleas of Mr Sterling and other Republicans.
On Friday night he continued to re-tweet comments and videos from right-wing political pundits casting doubt on the election results in Georgia and other states.