The YSL pioneer has been incarcerated since May.
"I don't wanna get tired of you, I'm in the box and we way at the top," raps Gunna in the self-directed video.
"When I was free, I was good and kind to the community around me and, when I am released, I will do the same."
The music executives aim to reach 5000 signatures or more.
Prosecutors were recorded reading YSL lyrics out loud in court as part of evidence.
The bill is currently in the process of becoming a law.