The proposed 30,000 all-seater arena at Ashton Vale is under threat amid plans to turn the site into `village green status`.
City have launched an e-petition, targeting 30,000 signatures, and the rugby club have leant their support to their football counterparts.
"This campaign is hugely significant to Bristol's sport and leisure culture," chief executive of Bristol Rugby Steve Gorvett told City's official website.
"It will give the region the opportunity to compete with leading stadiums across the world in hosting international sporting events and it is probable the new stadium would host Rugby World Cup matches in 2015.
"We have a chance to have a world-class sports facility, which will attract worldwide visitors and increased spending power to the region and will raise Bristol's profile in the eyes of potential investors."