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

New First-Year Students Scholarships
Total Worth: $5,000 to $20,000
Eligibility: $5,000 to $20,000
Minimum Criteria: based on the applicant’s grades in academic classes, the strength of the applicant’s curriculum and on the applicant’s best standardized test scores
Requirement for maintenance: maintenance of satisfactory academic progress
Separate application needed: No

Drew University provides aids at an average of 44763 per student meeting 85% of students need. 100% of students with need receive financial aid at an average of 40105 need-based grant. They also provide other scholarships including Civic Engagement Scholarships and Drew Scholarship in the Arts.