Taylor Swift & Celeb Friends: Cops Investigating Twitter Death Threats

Taylor Swift and her superstar posse are under attack from an Internet troll who's threatening to kill them ... and cops are on the hunt for the guy.

We've learned the guy has terrorized Taylor, saying, "I will kill some of you." He also targeted Gigi Hadid, tweeting, "people gon die they're gon die die die die!" And Cara Delevingne was targeted ... "I will kill your friends and I am excited about it."

Chrissy Teigen, who's not part of Taylor's posse, was also in the lunatic's crosshairs, with this ... "gonna give it one shot, but I probably gonna end up murdering your friends."

Law enforcement sources tell us they first got the heads up about the cyber threats from director Kyle Newman, whose wife, Jaime King, was also on the receiving end of threats.