I am about to enter my first year of a doctoral program in sociology
and need more information on available scholarships.  Since my GRE
scores were rather high, I am interested in scholarships that award
funding primarily based on GRE scores.  Would you be able to provide a
list of these?

Usually, no scholarhips are awarded based on just the GRE scores.
However, with a high score, you would be a more desirable candidate
for the school and they would be more likely to make a scholarship
offer to you. Typically, most doctoral students depend on
assistantships where they put in 20 h of work every week and get
stipends, benefits, and reduced tuition rates. This stipend is usually
more than enough to cover all living and educational expenses. The
best chance of getting such assistantships is by applying to large
state schools. Look at Ohio state, Univ. of Texas, and Texas A&M in
particular.