Sen. Marco Rubio (R-Fla.) and former Hewlett-Packard CEO Carly Fiorina are tied for third place with 8 percent. Sen. Ted Cruz (R-Texas) follows with 6 percent, then former Florida Gov. Jeb Bush with 4 percent.
The poll attributes Trump’s popularity to his stance on immigration.
Among respondents who said they prefer a candidate a plan to deport illegal immigrants in the country, 34 percent support Trump. Carson is second in this group with 16 percent.
Among those who dislike candidates with such a stance, only 13 percent support Trump — second-most in the field, after Carson's 17 percent.
Other measurements in the poll reflect this divide in the Republican Party over the issue of immigration.
Eighty-four percent of those who favor mass deportation say immigration is the most important issue in the 2016 election, while only 44 percent of respondents who do not favor deportation say immigration is their top priority.
The poll also highlights voters’ well-documented preference for an “outsider” candidate.
Sixty-six percent of GOP voters say they are more likely to vote for a candidate who brings new ideas and different approaches to Washington, compared to 29 percent who say experience and a proven record in government are more important to them.
The poll was conducted in an open-ended format, in which respondents were asked to name their preferred candidate, rather than choose one from a list.
The survey questioned 421 Republicans in telephone calls from Sept. 22-27 and has a margin of error of 5.5 percent.