A spokesman for the Judicial Office said Nick Harrington had resigned with immediate effect.
The anti-Irish tweet appeared on the Warwick district councillor's now deleted account during the Eurovision Song Contest but was widely retweeted.
Other tweets on the feed which "may have caused concern" are also being looked at, Warwickshire Police said.
Police confirmed on Sunday they were investigating the tweet, which contained offensive and racist language, and are treating it as a suspected hate crime.
More from Coventry and Warwickshire
On Monday, a spokesman said officers were aware of other tweets, posted on the same account, which may have caused concern.
"These will be considered during the investigation," the spokesman added.
The leader of Warwick District Council, Andrew Mobbs, said he was also aware of other comments and it was up to a formal standards committee to purse all avenues before coming to any conclusions.
Mr Mobbs had already suspended Mr Harrington, who represents the Stoneleigh and Cubbington ward, from the Conservatives on the district council for six months saying his behaviour was unacceptable.
The Judicial Office said magistrates are required by the terms of their declaration and undertaking to inform their bench chairman and justices' clerk if they are subject to an investigation by the police.
An advisory committee will then consider whether a conduct investigation is required.
The national Conservative Party has suspended Mr Harrington, pending an investigation.
The district council has said it will wait for the police investigation to conclude before deciding what, if any, action to take.
A Tory councillor being investigated over a racist tweet which appeared on his account has quit as a magistrate.