Yeah, Ohio State University-Main Campus does provide scholarships based on merit. Here are some of them:

Eminence Fellows Program and Scholarship
Total Worth: Full cost of attendance plus a $3,000 enrichment grant accessible after the first year of successful study
Eligibility: Full cost of attendance plus a $3,000 enrichment grant accessible after the first year of successful study
Minimum Criteria: Strong standardized test scores and GPA and top 10 percent (and above) class rank with curiosity as demonstrated by research or equivalent experiences
Requirement for maintenance: Minimum GPA of 3.4/3.5 (based on program of study) measured at the end of the first year and annually thereafter
Separate application needed: Yes
Application deadline: November 9

National Buckeye Scholarship
Total Worth: $13,500 per year
Eligibility: $13,500 per year
Minimum Criteria: Top 25 percent of their graduating classes with an ACT composite score of 29 or higher or SAT score equivalent of 1330 or higher
Requirement for maintenance: Minimum GPA of 2.5 measured at the end of the second year and annually thereafter
Separate application needed: No
Application deadline: November 1

Maximus Scholarship
Total Worth: $3,000 per year
Eligibility: $3,000 per year
Minimum Criteria: Top 3 percent of their graduating classes with an ACT composite score of 33 or higher or SAT score equivalent of 1450 or higher
Requirement for maintenance: Minimum GPA of 3.2 measured at the end of the second year and annually thereafter
Separate application needed: No
Application deadline: November 1

Ohio State University-Main Campus provides aids at an average of 14976 per student meeting 73% of students need. 99% of students with need receive financial aid at an average of 11497 need-based grant. They also provide other scholarships including Aida Cannarsa Snow Endowment Fund Scholarships.