Cristiano Ronaldo wants his rape case to be taken out of the public eye ... the soccer superstar is asking a judge to force the civil case against him to go to a private forum.
It's all in new court docs obtained by TMZ Sports ... which show Ronaldo wants his lawsuit with his rape accuser to move from federal court to a private independent arbitrator.
Ronaldo says because Kathryn Mayorga agreed to a settlement and a non-disclosure agreement in 2010 after accusing him of rape in 2009 ... she should be compelled to at least try to litigate the dispute in arbitration.