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

President’s Excellence Scholarship
Total Worth: fully funding tuition, room and board for four years and providing a $500 per semester book allowance and a $1,000 stipend each semester
Eligibility: fully funding tuition, room and board for four years and providing a $500 per semester book allowance and a $1,000 stipend each semester
Minimum Criteria: a composite score of 28 or above on the ACT or its equivalence on the SAT (1250 and above, reading and math only) and a 3.0 or better high school cumulative grade point average
Requirement for maintenance: a 3.0 or above cumulative GPA

Provost Scholar Scholarship
Total Worth: room, board, tuition and a $400.00 per semester book allowance
Eligibility: room, board, tuition and a $400.00 per semester book allowance
Minimum Criteria: a composite score of 24-27 on the ACT or its equivalence on the SAT(1090-1240 reading and math only) and a 3.0 or better high school cumulative grade point average (GPA)
Requirement for maintenance: a 3.0 or above cumulative GPA

University Scholar Scholarship
Total Worth: tuition and also provides an additional $200.00 for books per semester
Eligibility: tuition and also provides an additional $200.00 for books per semester
Minimum Criteria: 22 or 23 on the ACT or its equivalence on the SAT(1020-1080 reading and math only) and a 3.0 or better high school grade point average (GPA)
Requirement for maintenance: a 3.0 or above cumulative GPA

They also provide other scholarships including Frank Boulware, Sr. Legacy Scholarship.