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

College Deans’ Scholarships
Requirement for maintenance: Remain in good academic standing
Separate application needed: No
Application deadline: February 1

Père Marquette Award
Requirement for maintenance: Remain in good academic standing
Separate application needed: No
Application deadline: December 1

Burke Scholarship Program
Total Worth: Full tuition plus stipend depending upon student need
Eligibility: Full tuition plus stipend depending upon student need
Minimum Criteria: ACT composite of 25 or SAT of 1150 with a passion for social justice and a commitment to serve others
Requirement for maintenance: Maintain a 3.0/B GPA, meet program requirements, and live on campus for the first two years
Separate application needed: Yes
Application deadline: February 1

Marquette University provides aids at an average of 29812 per student meeting 76% of students need. 100% of students with need receive financial aid at an average of 24753 need-based grant. They also provide other scholarships including Boys and Girls Clubs/Urban Scholars Program and Diederich Scholarship.