Some schools require seperate applications for admission and scholarship, other do not.
I know three selective schools offers large amount of merit scholarships regardless of citizenship. Washington and Lee has Johnson Scholarhip. Vanderbilt has three different scholarships. Washingto University at St. Louise offers Danforth Scholarship, which requires students to be nominated by a school offiical.
You can also check out the Coco-cola scholarship, at http://www.coca-colascholarsfoundation.org/applicants/#programs
http://www.wlu.edu/johnson-program/faqs
http://admissions.wustl.edu/scholarships-financial-aid/Freshman-Academic-Scholarship-Fellowship-Programs/Pages/The-Danforth-Scholars-Program.aspx
http://www.vanderbilt.edu/scholarships/ingram.php