The company behind a Justin Bieber themed mobile app is firing back at the Biebs -- insisting the Constitution protects its right to lampoon the crap out of anyone it wants.

TMZ broke the story, Bieber sent a cease-and-desist letter to the creators of "Joustin' Beaver" -- claiming the company is trampling all over Justin's trademarks.

But now, the company in question -- called RC3 -- is calling the singer's bluff ... filing its own preemptive lawsuit against Bieber, asking a court to declare RC3 is not violating any laws by poking fun at him.

According to RC3, the game is a "parody" protected by the First Amendment to the U.S. Constitution.