Yeah, Georgia State University does provide scholarships based on merit. Here are some of them:

Presidential Scholarship
The Goizueta Foundation Scholars Fund
Total Worth: $22,000-$31,000 per year
Eligibility: $22,000-$31,000 per year
Minimum Criteria: GPA of 3.96, SAT of 1431 and ACT of 32.5
Separate application needed: Yes
Application deadline: November 15

Zell Miller Scholarship
Total Worth: Tuition and fees
Eligibility: Tuition and fees
Minimum Criteria: Based on Leadership, Community Service, Extracurricular, school and community-related activities/participation, Financial Need, High School GPA, The Goizueta Foundation Scholarship Essay, SAT or ACT scores and Personal Resume.
Application deadline: March 12

Georgia State University provides aids at an average of 12541 per student meeting 54% of students need. 96% of students with need receive financial aid at an average of 5276 need-based grant.