"I have never had weed a day in my life, so immediately after I started drinking it, I started to feel weird and it didn't taste like something I recognised," Mr Brown said.
Mr Brown also ordered chicken nuggets and a cheeseburger, but these items reportedly weren't spiked.
Mr Brown said he felt "high as a kite," and was "panicking" while at his job, so he called his dad who urged him to contact police, and tell his manager what had happened.
The young man claimed he had a difficult time convincing authorities of what had occurred, but once an officer responded and viewed the bags in the cup, they corroborated the substance appeared to be marijuana.
An investigation into the incident is ongoing, according to Major Bob Bromage, from the Beaufort County Sheriff's Office spokesman. He didn't specify which particular McDonald's restaurant was being investigated over the allegations. The marijuana found in the drink has been submitted for evidence.
A representative for McDonald's in the US said the company is "fully co-operating with law enforcement on the validity of this claim".