Rokoduguni was forced to go under the surgeon's knife in December and his place in the England side for the upcoming Six Nations is up in the air.
It is unclear exactly when the winger will return and so the West Country outfit have bolstered their ranks by the addition of the former Worcester man.
Vuna made 31 Premiership appearances for the Warriors between 2015 and 2017 and Bath director of rugby Todd Blackadder was delighted with his capture.
"To be able to bring in a player of his calibre at this stage of the season is a real boost for us," he told the club's website.
The Auckland-born flyer was delighted to strap his boots on once more and hopes to make a real impact in his new surroundings.
"I am really excited that the opportunity to join Bath has come up," said Vuna. "There is a lot to play for, and I am looking forward to getting out there on the pitch and making a difference when I get an opportunity."