The Hill reported Capitol Police were looking into the post by someone identifying himself as Troy Gilmore Jr.
The tweet, posted early Friday, said, "Take down Ted Cruz, at his home" and listed Cruz's home address in Houston, The Hill reported.
It also said, "What goes around comes around CRUZ!!"
The Hill said the poster -- using the Twitter handle @ArmyVet54 -- said he had served in the U.S. Army and Navy, and posted another tweet Friday afternoon saying Cruz "needs tobe [sic] taught a street wise [sic] lesson."
"We're aware of it and have alerted the proper authorities," Cruz spokesman Sean Rushton told The Hill. "I can't comment further on security matters."
The report said the author had posted Cruz's home address several times this month, using threatening language.
The Hill said @ArmyVet54 has no followers on Twitter.