The trial of Brandon Ziobrowski opened Monday in federal court and is expected to continue through the week.
He pleaded not guilty to using interstate and foreign commerce to transmit a threat to injure another person last year.
Authorities say the then-33-year-old Cambridge, Massachusetts, resident tweeted last July "I am broke but will scrounge and literally give $500 to anyone who kills an ICE agent."
Ziobrowski also allegedly tweeted he wanted to "slit" the late U.S. Sen. John McCain's throat.
His lawyers argue his comments are constitutionally protected political speech.
Federal prosecutors say Ziobrowski’s comments represent a “true threat” not protected by the First Amendment.