Organised by the RIBA, the competition is calling for architects to develop the college's Battersea Bridge Road site adjacent to the Sculpture Building.
The RCA is hoping the scheme will become a substantial second site just two miles south of its main Kensington Gore campus.
The space created will be used for teaching, research and business-related activities, as well as a range of support services.
From the initial expressions of interest, nine design teams will be invited to attend an interview. Following that, between four and six practices will be asked to take part in the design concept stage of the competition.
To enter the competition contact the RIBA Competitions Office on 0113 234 1335 or visit www.ribacompetitions.com.
Deadline for entries is midday on Wednesday, 6 September.