Provisional results indicate that Dr. Rawlings polled 2,403 defeating incumbent Member of Parliament Nii Armah Ashietey who had 1,348 votes.
A third contestant Nii John Coleman had 100 votes.
Dr. Rawlings' victory comes after she struggled to cast her vote in Saturday's election after her name was missing in the voters’ register.
All attempts to trace her name to vote in the primaries have proved futile after touring several polling stations to trace her name.
Meanwhile, Accra Mayor Alfred Oko Vanderpuije has also won the Ablekuma South constituency.
The Chief Executive Officer of the Accra Metropolitan Assembly polled 3,298 while his contender Wisdom Nii Amo Dodoo managed 1,259 votes in Saturday's polls.
Mr. Vanderpuije takes over from incumbent Fritz Baffour who decided not to seek re-election.