The 18-year-old, who joined Albion in 2022, signed her first professional deal with the Women's Super League side in April, and now she is in with a shot of some first-team football.
The centre-back said she was thrilled to join the Scottish Women's Premier League side and said there are similarities between them and Albion.
She told Rangers' website: "I am very happy to be here. Rangers is a great club with a great culture, so I am really excited to get started.
"Rangers and Brighton share a lot of principles in terms of wanting to play attractive football, being a possession-based team.
"I am also a young player, so I am hoping to get experience in senior football and try to get some minutes to keep improving."
Pegram has made 39 appearances for Albion's under-19 side to date. Now, Rangers head coach Leanne Crichton is looking forward to working with the "talented" youngster.
She said: "We’re really pleased to welcome Jess to Rangers for the rest of the season. She’s a talented young player with great potential, and we believe this is a fantastic environment for her to continue her development."
Albion Under-19s head coach Danielle Bowman said this was a "fantastic" opportunity for the defender to help her progress with her career.
While Albion's Women's and girls' academy manager, Perry Northeast, expressed his "excitement" at this opportunity for Pegram.