Abbott leads Davis 29 percent to 21 percent in the survey conducted for Texas Lyceum, a nonpartisan, nonprofit group. Fifty percent of voters said they "don't know" who they will support.
Davis, who became a national figure when she filibustered an abortion bill this year, is expected to announce her campaign Thursday. Abbott has already announced that he is running in the open race.
Given the strong Republican tilt in Texas, Abbott's fundraising strength and his deep support from conservatives, he begins the race as a very substantial front-runner in the eyes of most observers.
The poll was conducted over a two-week period, from Sept. 6-20. That's a longer sample period than typically used by pollsters.