Romney put the 42-year-old conservative chairman of the House Budget Committee on the ticket Aug. 11. The AP-GfK Poll was conducted Aug. 16-20.
Romney and Ryan will be crowned as the GOP presidential and vice presidential nominees next week at the Republican National Convention in Tampa, Fla. The Democrats hold their convention the following week in Charlotte, N.C.
The closely locked contest reflects deep partisan divisions across the country.
Among true independents, those who say they do not lean toward either party, the share of undecided voters is declining, with each candidate picking up new support at about the same pace. However, Romney maintains a small advantage with the group, with the backing of 41 percent of independents to Obama's 30 percent. Some 21 percent still say they support neither candidate.
Among all voters, 23 percent are undecided or say they have not yet committed to their candidate.