The former director of Vote Leave published a 2,900-word advert aimed at mathematicians, data scientists, economists, software developers and PR experts.
One of the successful applicants will get to work as Mr Cummings’ personal assistant for a year, according to Thursday’s post on his blog.
“We want to hire an unusual set of people with different skills and backgrounds to work in Downing Street with the best officials,” he wrote.
It follows reports that Boris Johnson is planning “seismic” changes to the civil service following last month’s general election victory.
Mr Cummings, a long-standing critic of Whitehall, has in the past said the principle of a permanent civil service was “an idea for the history books”.
In his blog he claimed there were “some profound problems at the core of how the British state makes decisions”.
“We want to improve performance and make me much less important — and within a year largely redundant,” he said.
“At the moment I have to make decisions well outside… my ‘circle of competence’ and we do not have the sort of expertise supporting the PM and ministers that is needed.”
Mr Cummings warned applicants for the post of his personal assistant that they would have to sacrifice nights and weekends to make his life easier.
“Frankly it will hard having a boy/girlfriend at all,” he added. “It will be exhausting but interesting, and if you cut it you will be involved in things at the age of 21 that most people never see.
“I want people who are much brighter than me who can work in an extreme environment.”
In another section aimed at “super-talented weirdos”, he wrote: “We need some true wild cards, artists, people who never went to university and fought their way out of an appalling hell hole”.
And after asking applicants to send their CV by email, he warned “I’ll bin you within weeks if you don’t fit — don’t complain later because I made it clear now.”
Mr Cummings ended the post by admitting that his job advert was a “fast and cheap way to get ideas”.
The general secretary of the FDA union, which represents senior civil servants, warned that the plan would threaten the impartiality of the civil service.
Dave Penman said: “Civil servants are recruited on merit, not patronage – a critical principle if they are to provide the best impartial advice to ministers.
“It would be ironic if, in an attempt to bring in radical new thinking, Cummings was to surround himself with like-minded individuals – recruited for what they believe, not what they can do – and less able to provide the robust advice a minister may need, rather than simply the advice they want.”
Additional reporting by Press Association