Are there any scholarships for a high GMAT score? For example if one gets a 770 score.?

Yes, you can apply for merit-based scholarships for MBA through your high GMAT Scores.  Merit-based scholarships are granted to students with excellent academic records or students having extraordinary achievements in extracurricular activities or sports. Here, the financial background of a student does not hold much relevance. There are various universities and educational institutes that offer MBA scholarships for Indian students. If you have good academic credentials apart from GMAT Scores like a high CGPA in UG, and a good 12th-class percentage then you have a good chance of getting a scholarship.

Top universities abroad offer scholarships on GMAT scores like Harvard, Stanford, and Wharton.

TOP UNIVERSITIES FOR MBA -

Harvard University
Columbia University
Oxford Said Business School
Kellogg 
London Business School
MIT Sloan
INSEAD

NOTE -
You must avoid these mistakes while applying for the GMAT scholarship - 
Do not write a generic statement of purpose (SOP).
Don’t avoid the guidelines specified in the application process.
Don’t be inconsistent.
Be clear about your future expectations.

I hope this helps or else you can directly talk to an expert here!