The poll the first in which Cruz has led the field, shows the Texas senator with 24 percent support from voters who intend to take part in the February 1, 2016 Iowa caucuses, the first real measure of voter support in the 2016 presidential campaign.
As recently as October, Cruz, 44, had just 10 percent support in the Monmouth poll.
His fortunes have changed, however, after a critical endorsement from a popular Republican lawmaker in this heartland state, and as voters cool on retired neurosurgeon Ben Carson, an earlier favourite.
“This marks the first time Ted Cruz has held a lead in any of the crucial early states,” said Patrick Murray, director of the independent Monmouth University Polling Institute in West Long Branch, New Jersey, highlighting what he called a “Cruz surge in Iowa.”
As Ben Carson’s stock has fallen, Cruz has been able to corral most of those voters, Murray said.
Billionaire real estate mogul Donald Trump was the second choice of Iowa Republicans with 19 percent support, followed by Marco Rubio (17 percent); Ben Carson, (13 percent); Jeb Bush, (six percent); Rand Paul (four percent) and Carly Fiorina and John Kasich each with three percent.
Two months ago, Carson topped the Monmouth survey with 19 percent support, but his poll numbers have been in free-fall in recent weeks following a number of gaffes in the area of foreign policy and security.
His slip-ups have occurred at precisely the moment when Americans are paying more attention to candidates’ foreign policy acumen because of perceived security threats abroad and at home.
Marco Rubio, the fresh-faced senator from Florida, is seen by many as the favourite of the party establishment given the lackluster showing on the campaign trail so far of his state’s former governor Jeb Bush.
Like Cruz, he appears to have improved his standing with Iowa voters, increasing his support by seven percentage points since the last poll, up from 10 percent in October.
The telephone survey of 425 likely participants in the Iowa caucuses has a margin of error of plus or minus 4.8 percent.