The Game Says He Banged Kim Kardashian

First came Ray J ... then came The Game ... who just decided to announce he bangaranged Kim Kardashian long before she was super famous.

It's the humble brag of the century -- Game was doing an interview for some UK radio station, when the topic turned to rumors he's been hooking up with Khloe in the wake of her split from Lamar Odom.

Game denied the rumors -- but said he is NOT a Kardashian virgin ... casually letting it slide that he got it in with Kim way back in the day.

Game didn't say when exactly -- but sources tell TMZ, Game and Kim hooked up briefly in 2006.

Kim's infamous sex tape was released a year later, but to Ray J's credit ... it was taped in 2003.

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