Galway City Councillor Owen Hanley posted a message on Facebook saying he intended on resigning his seat while the allegations are “investigated fully by the appropriate authorities”.
“In the past 48 hours certain allegations have been made about me,” Mr Hanley said.
“These are very serious matters and will obviously take a considerable length of time to be investigated fully by the appropriate authorities.
“In these circumstances I believe that the correct thing for me to do is to resign my members (sic) of Galway City Council,” he added.
Mr Hanley said he did not propose making any further comment in relation to the matter.
The allegations which led to the councillor taking the decision centre on claims he used an anonymous account on Twitter.
The claims were made by a former member of the party.
Mr Hanley previously denied using a fake social media account when contacted by his party.
He did not respond to requests for comments from the Irish Independent.
In a statement, the Social Democrats said it is appropriate that Mr Hanley resigned while the allegations are investigated.
“When the party first learned of allegations, the whip was removed from Mr Hanley and he has now resigned his membership of the Social Democrats,” a spokesperson said.
“The party notified the relevant statutory authorities charged with investigating these allegations as soon as it became aware of them.
“The party takes allegations of this nature extremely seriously and has at all times strictly adhered to our statutory obligations.”
The Social Democrats contacted gardaí and Tusla about the allegations.
Gardaí said they are aware of the claims. However, it is understood they have not received any formal allegation or complaint from anyone involved at this point.
On the Social Democrats website, Mr Hanley was described as a “fresh and progressive voice” on Galway City Council.
It said he has been involved in campaigning activism and community work for years.
The profile was online yesterday but has since been removed by the party.