3 things to make a static Sinatra App and upload to Heroku

1) Create a file app.rb with this code:

require 'sinatra'

get '/' do
    File.read(File.join('public', 'index.html'))
end

2) Create a Gemfile

source 'http://rubygems.org'
gem 'sinatra', '~> 1.3.2'

3) Create a config.ru

require "./app"
run Sinatra::Application

Then just create your Heroku app, commit and push.