The Archbishop of Vienna claims militants killed the Indian priest, who was kidnapped during a raid on a nursing home in Yemen, on Good Friday.
Although the claims cannot be verified Islamic State has been known to crucify Christians in Iraq and Syria.
Father Thomas Uzhunnalil was taken by the group during an attack on an old people's home in southern Yemen.
Cardinal Schönborn, told the Easter Vigil Mass in St Stephen's Cathedral in the Austrian capital that the priest had been crucified.
Mr Trump, who is hoping to be the Republican candidate for president in November's election, posted a link to the story on his Facebook page.
"Terrible! And we cannot water board?" He questioned.
In February Donald Trump said if elected he would do "a hell of a lot worse than waterboarding" to anyone accused of terrorism.
On another occasion he said: "On the other side they chop off our young people's heads and they put them on a stick. Would I approve waterboarding? You bet.
"I would approve more than that and don't kid yourself folks, it works. Only a stupid person would say it doesn't work."