Joe Rogan talked with cops after Liver King challenged him to a fight via social media ... and Joe told police the fitness influencer appeared to be "significantly unstable."
According to new legal docs, obtained by TMZ, cops in Austin, Texas say the former "Fear Factor" host told them he interpreted Liver King's string of social media rants as threatening ... which is why cops were called and eventually led to LK being arrested on a charge of making a terroristic threat.