Just got some ideas from zurb-foundation gem and fetched javascript files from http://cdnjs.com and made jquery available in any rails project, or even just project with sprockets support.

1. gem 'fresh-backbone' in your Gemfile
2. //= require underscore, backbone and jquery from your application.js
3. Have your backbone as you like

1. gem 'fresh-backbone' in your Gemfile, yep
2. Gemfile in your sinatra project:

source "https://rubygems.org"

gem "sinatra"
gem "sinatra-asset-pipeline"

gem "sprockets"    # This line should go before asset gems!
gem "fresh-backbone" # The gem you're trying to use

3. In your sinatra application:

Bundler.require

require "sinatra/asset_pipeline"
require "erb"

register Sinatra::AssetPipeline

get "/" do
    erb :index
end

4. Run application and have backbone files!