Abbott Mead Vickers BBDO was the previous incumbent, but the business has moved to Rapier without a pitch.
The change consolidates RAC's integrated business at Rapier following the agency's capture in May of the digital and direct marketing account.
AMV, which had worked on the RAC account for six years, will continue to handle brand advertising for Aviva.
David Tyers, the sales and marketing director at RAC, said: "RAC has ambitious plans for the next few years, and in Rapier I believe we have found the right partner to work with us to realise our ambitions across all areas of our brand and marketing communications."
Jonathan Stead, the chief executive of Rapier, said: "RAC is a great British brand with enormous potential. We look forward to helping it become one of the most dynamic and modern service businesses in the UK."
Last month, Aviva sold RAC for £1bn to the US private equity company The Carlyle Group as part of its strategy to focus on its insurance and savings business.
However, Aviva said that it will maintain a marketing partnership with RAC following the deal, which is due to go through in September.