Trump was addressing a campaign rally on Saturday at Pittsburgh International Airport near Pittsburgh, Pennsylvania.
A Trojan horse is a mythological wooden statue in which ancient Greeks are said to have concealed themselves in order to enter the city of Troy.
Trump has repeatedly warned that the US should not accept Syrian refugees.
He has also accused US President Barack Obama of purposefully funneling refugees into states with sizeable Republican votes.
Trump, a billionaire businessman from New York, has propelled himself as the presumptive Republican nominee by framing himself as an anti-establishment outsider.
However, his campaign has been defined by controversy from the beginning, including disparaging remarks about women, Mexican immigrants and Muslims.