Lorcan Halton, 45, from the Saracen area, was arrested in County Cavan and is being held by police.
Scots officers appealed for help after he failed to turn up at court on January 15.
He was last seen in Cairnryan, Dumfries and Galloway, on January 9, where he boarded a ferry to Belfast.
Police warned members of the public not to approach him.
A spokeswoman for Police Scotland said: "Further to our previous appeal regarding missing registered sex offender, Lorcan Halton from the Saracen area in Glasgow, he has been traced in County Cavan, Ireland."