Rodrigues made her international debut in 2018 and averages 21.22 in one-day-internationals and 26.37 in Twenty20s.
England World Cup winner Lauren Winfield-Hill and Australia wicketkeeper Alyssa Healy are also in the Superchargers squad.
Also joining Superchargers are bowler Phoebe Graham and batter Ami Campbell.
Trent Rockets have boosted their squad with the signings of all-rounders Alicia Presland and Teresa Graves, while right-arm medium pacer Grace Gibbs has linked up with Oval Invincibles.
The moves end the second phase of the player selection process in the women’s competition. Phase three, throughout June, will see the eight teams finalise their 15-strong squads.
The first match of the tournament – a women’s fixture between Oval Invincibles and Manchester Originals – will be live on BBC TV.
Both the men’s and women’s finals take place at Lord’s on Saturday, 21 August.