Angela Rye has been targeted with menacing and derogatory threats in recent months.
The CNN political analyst said she has received annoying, harassing and threatening messages on her phone, social media and email, according to court documents reported by TMZ.
The messages started after she started dating the rapper Common over the summer, although the couple didn't go public with their relationship until last week.
Rye said the derogatory messages started out as annoying, but grew more menacing -- and included references to locations she and Common visited privately over the summer.
"Yr dumb dead ass gonna be found in a river," read on message sent Aug. 5. "Let me catch ya ass I'm put the paws on ya."
Los Angeles police obtained search warrants to examine social media posts by the suspect, whose screen name has been identified.
The incident remains under investigation.