The winner will fill the Senate District 13 seat previously held by state Sen. Greg Kirk, a Republican from Americus, who died in December after he was diagnosed with bile duct cancer.
The election was one of the first where voters used Georgia's new voting system, which combines touchscreens and printed-out ballots. The system was previously tested during local elections in six counties in November and in a state House election last month.
Summers previously ran for state Senate in 2002. Quinn finished in second place in a special election for a state House seat in November.
Senate District 13 covers Crisp, Dodge, Dooly, Lee, Tift, Turner and Worth counties, as well as parts of Sumter and Wilcox counties.
After next month’s runoff, the seat will be on the ballot again for a regularly scheduled election in November.