R. Kelly is taking Uncle Sam to court -- 'cause he claims federal prison officials leaked a bunch of his private info to an Internet blogger ... who aired a lot of his laundry.

The incarcerated singer just filed a lawsuit against the U.S. government, a handful of Bureau of Prisons workers, and Tasha K ... all of whom, he claims, were in cahoots to publicize his private matters while he was in custody out in Chicago during his case there.

Kelly points the finger at three unnamed BOP officials at the prison he was being held at, alleging they accessed their internal system that documented what Kelly was doing within their walls ... including email correspondence, private calls, visitor logs, etc.

Kelly and his lawyer, Jennifer Bonjean, believe the officials struck an agreement with Tasha K to supply her with Kelly's personal info ... which he suspects might've been done for cash. Tasha has already addressed these claims -- which Kelly publicly made well before this suit -- and denied being mixed up in any illegal activity.

Kelly claims the info allowed Tasha -- who has a big YouTube following -- to publish unflattering pieces about RK ... which he says has hurt his rep, invaded his privacy and caused him undue emotional distress.

Kelly says the U.S. government was negligent in allowing its prison personnel to allegedly access and share this info ... and now he's asking for major damages.

BTW, the claims Kelly is making here date back to 2019 or so. Since being convicted in his Chicago case, he has been moved to a federal facility in North Carolina -- where he's serving his lengthy sentence.