The YouTube video shows Ford talking to several people at a Steak Queen restaurant Monday night, the Canadian Broadcasting Corp. reported. The clip shows him using the word "bumbaclot," a profane Jamaican slang term, several times.
Ford, who has pledged multiple times that he has quit drinking since it was revealed last year he used crack cocaine while in office, told reporters Tuesday he had been drinking "a little bit, yeah."
Ford said he did not think his Jamaican accent was offensive, the CBC said.
"I met some friends. If I speak that way, that's how I speak with some of my friends and no, I don't think it's discriminative at all," he said. "It's my own time."
While mumbling at times in the video, Ford also speaks about how he's been under "counter surveillance."
"They're chasing me around five months," he can be heard saying at one point before eventually declaring "I'm a straight-up guy" before leaving with his takeout order.
Ford, 44, is running for a second term this fall.