Mr Cruz overcame billionaire rival Donald Trump and fellow senator Marco Rubio to become the Midwestern state's favourite to lead the Republican party in the November presidential elections.
It's thought more than six-in-ten of Republican party caucus-goers in Iowa were evangelical Christians, many of whom are thought to have supported Cruz in his opposition to abortion and gay marriage.
Revd Sally Foster-Fulton, who is American and currently works for the Church and Society Council of The Church of Scotland, said she was not surprised by Donald Trump's defeat.
Speaking on Premier Christian Radio's News Hour programme, she called for US politicians to be motivation by a gospel bias for the poor.
Thank you Iowa! This is OUR time. Join us: https://t.co/YBcXsTJlj4 pic.twitter.com/hrHfyyo253
— Ted Cruz (@tedcruz) February 2, 2016
Revd Foster-Fulton said: "What are these candidates going to do for the people falling through the cracks economically, folk falling through the cracks in regards to the health system, what about folk in others parts of the world who are paying off debts?
"Those are the questions that I would ask. We need to be driven by our gospel bias for the poor.
"If you've got a candidate who is going to be divisive and continue with the fractures that we already have and turn them into big, gaping holes, than I think they need to think again.
"So my prayer would be for grace, for finding a candidate and a party that can bring some grace and some peace to the United States and to the world."
Meanwhile, Hillary Clinton finished just half a per cent ahead of Bernie Sanders in the Democratic contest in Iowa.
New Hampshire is the next state to vote in a week's time.
Both the Republicans and Democrats will choose their presidential contenders in party conventions this summer.