In a head-to-head matchup with Republican front-runner U.S. Rep. Ernest Istook, 58 percent said they would vote for the incumbent.
The survey of 773 registered voters, taken Jan. 27-30 by Oklahoma City-based SoonerPoll.com., showed 76.2 percent approved of Henry's performance, with 15.5 percent disapproving.
The poll sponsored by the Tulsa World and KOTV-Channel 6 has a 3.5 percent margin of error.
A June Oklahoma Poll saw Henry with a 72 percent approval rating.
“I think he's done a good job,” said Steven Hofferber, a Tulsa Republican who responded to the poll. “He hasn't done anything to make me mad. He's for education and doing something about the roads and bridges, and he seems to be on top of those things.”
Poll consultant Al Soltow said the drop-off in the head-to-head poll was among Republicans.
“Sixty-four percent of the Republicans say they approve of the job Henry is doing, but only 25.7 percent said they would vote for him,” Soltow noted.
That number may reflect indecision among Republicans. When asked their preference in the three-way GOP primary that includes Istook, Tulsa businessman Bob Sullivan and state Sen. James Williamson, 43 percent didn't know or refused to answer.
The poll results for Republicans has a 5.7 percent margin of error.
Sharon Emigh of Sand Springs said she makes a special effort to be politically informed, but doesn't know enough about the Republican gubernatorial candidates to form any opinions.
“I really want to know what they stand for,” she said. “I look for a righteous person, a moral person, who is interested in passing laws to make the state of Oklahoma safe.”
Voters also were uncertain about the three Republican and two Democratic candidates for lieutenant governor.
Almost two-thirds of Republicans didn't know or refused to answer when asked for their preference from among House Speaker Todd Hiett and state senators Scott Pruitt and Nancy Riley. Hiett was named by 18 percent, Pruitt by 12 percent and Riley by 8 percent.
More than three-fourths of Democrats said they had no preference between state Rep. Jari Askins and former congressional aide Peter Regan. Askins tallied 19 percent, Regan 5.
Information from: Tulsa World, http://www.tulsaworld.com