Kirk Kus – who is now 26 but sent the tweet when he was 19 – used a phrase considered offensive in a thread on the social media site.
His account was deactivated shortly after Sheffield blog the South East Echo informed the Brexit Party about the tweet.
Mr Kus was elected as a UKIP councillor for the Alvaston ward in Derby last May but later defected to the Brexit Party in July along with four other UKIP councillors.
On his website, Mr Kus states he is from a ‘working-class and Polish background’, and describes himself as ‘a democrat, patriotic and Eurosceptic’.
He also says, on the site, it is time for ‘ordinary people’ who are ‘in touch with the community and will put the country first’ to be elected.
Mr Kus would be one of the youngest members of parliament if elected and has a degree from Derby University.
The Brexit Party acknowledged the tweet was offensive, but said their candidate was responding to abuse and not giving it.
A spokesperson said: “This article deliberately misrepresents this tweet, ignoring the fact it is clearly a question with a question mark and part of a thread.
“The candidate is asking what the bizarre and offensive phrase, included in a previous tweet, means.
“The reporter chose to ignore this critical context, which they were informed of, to imply our candidate used the phrase approvingly.
“An early version of this article also omitted the fact the tweet was seven years old, shared shortly after the candidate turned 20, to imply it was recent.
“This is the lowest form of offence archaeology and the Brexit Party stands by the candidate, who was responding to abuse and not giving it.”
The row comes after a Brexit Party candidate for Stoke North was axed after he remarked that animal testing should be stopped and instead carried out on people who voted for Britain to remain in the EU.
Twenty Brexit Party candidates have already quit the party and thrown their support behind the Conservatives in the upcoming election.