The Aegis-owned agency won the account after a pitch against agencies including PHD and Initiative.
The hire is part of a process that will also include the appointment of an ad agency and a PR agency, which are yet to be confirmed.
The bulk of Rank Interactive's media buying has previously been handled in-house. Digital planning and buying, by Carat's sister agency Vizeum, is not affected.
Rank Interactive started the process in February and the early stages were handled by ISBA. Phil Gates, the company's marketing director, made the appointment.
Its parent company, Rank Group, has previously made use of sponsorship and partnership deals to support its brands. In 2010 and 2011, it signed separate three-year deals with FremantleMedia Enterprises to be the official gaming partner of ITV's Britain's Got Talent and The X Factor respectively.
Carat and Rank Interactive declined to comment.