Nothing special is required to run grackle with Sinatra. You just create a client instance when you need it and use it.
As for getting retweets, the grackle call just maps to the Twitter API endpoint[1]:
client = Grackle::Client.new(YOUR_OPTIONS) # configure with your authentication
client.statuses.retweets? :id=>NNN # Get retweets for some tweet with id NNN