The DPP is to appeal the seven-year suspended sentence handed down to Magnus Meyer Hustveit.
He was convicted in July of raping his then-partner Niamh Ni Dhomhnaill while she slept.
The victim waived her right to anonymity to criticise the sentence and thousands of signatures have been collected calling for an appeal.
Legal papers were lodged on Friday, on the grounds that the sentence was unduly lenient.
