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."

Peter Osbourne of no fixed address was charged with four counts of making hoax calls, Gloucestershire Police said.
It relates to calls made on Wednesday about Wiltshire Police Headquarters, Bristol Royal Infirmary, Weymouth sea front in Dorset and Bath bus station.
Mr Osbourne, 56, is due to appear before magistrates in Bath later. Avon and Somerset Police were also involved in the cross border operation.

Donaldson is back in training following a lengthy lay-off with a heel injury which has kept him out for the whole of Gianfranco Zola's 16 games in charge.
Wigan have lost Sam Morsy, who starts a two-game ban after being booked for the 10th time this season at Blackburn.
They are also waiting form a verdict on the severity of fellow midfielder Shaun MacDonald's knee injury.
MacDonald went off early at Ewood Park, but the Latics are hopeful he has not suffered ligament damage.
Boss Warren Joyce could be back in the Wigan dug-out having watched from the stand on Saturday after undergoing minor surgery.

10 June 2016 Last updated at 16:01 BST
The airport has been built in St Helena, which is in the South Atlantic Ocean, between Africa and South America.
The project has cost 285 million pounds and was due to open in May.
A test flight at the airport wasn't able to land because it set ofo the aircraft's warning system for high winds.
A disabled man's online appeal for work has been seen by thousands of people.
[NEXT_CONCEPT]
A man has been accused of making a series of hoax bomb threats.
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Birmingham City remain without Clayton Donaldson and Michael Morrison for the visit of Wigan Athletic to St Andrew's.
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An airport that was meant to open on a British overseas territory has been delayed because its too windy there.