Thomas Cullen, 20, who has Down's syndrome, posted the video having failed to find a job after several months of trying.
Since putting the clip on Facebook, his appeal has been viewed more than 28,000 times.
His mother Carolyn said she had not expected the video to attract the level of attention and was "hopeful" it would help her son.
Mrs Cullen, from Thirsk, said: "I posted it on Facebook just thinking that somebody might see it and think 'Oh, I know somebody [who can help]'. I did not expect the amount of hits and shares that it's had.
"I think people view somebody with a disability as not able to do the job, but it just needs somebody to give a little bit of extra time to them.
"Thomas just needs somebody who is prepared to give him a chance.
"I'm hopeful. I would like him to get a job and to lead a normal life like anybody else."
According to Mencap less than a fifth of the 1.4m people in the UK with a learning disability are in employment despite at least 65% wanting to work.
James Bolton, from the charity, said: "Unfortunately [Thomas'] story is all too common.
"I think there are all too often negative attitudes from employers and the public about what people with a learning disability can do. Very often it's due to a lack of understanding."
A disabled man's online appeal for work has been seen by thousands of people.