Is it possible to upload a simple html and javascript file structure to heroku?

A simple way is to masquerade the HTML app as a PHP App. Heroku properly identifies PHP apps.

1. Rename your index.html file to home.html.

2. Create an index.php file and include your entry html file. If your HTML entry file is named home.html as recommended, your index.php should look like:

   <?php include_once("home.html"); ?>

3. In your command line on the machine you are pushing from, type:

   git add .
git commit -m 'your commit message'
git push heroku master

Heroku should properly detect your app now as a php app:

-----> PHP app detected
-----> Bundling Apache version 2.2.22
-----> Bundling PHP version 5.3.10
-----> Discovering process types
       Procfile declares types -> (none)
       Default types for PHP   -> web

-----> Compiled slug size: 9.9MB
-----> Launching... done, v3
...

Mad Thanks to lemiffe for his blog post: http://www.lemiffe.com/how-to-deploy-a-static-page-to-heroku-the-easy-way/

Here is a more elegant method: Just add a file called package.json which tells Heroku to use harp as your server:

{
  "name": "my-static-site",
  "version": "1.0.0",
  "description": "This will load any static html site",
  "scripts": {
    "start": "harp server --port $PORT"
  },
  "dependencies": {
    "harp": "*"
  }
}

and then deploy to Heroku. Done!

Further information: https://harpjs.com/docs/deployment/heroku

You can use rack to do this:

https://devcenter.heroku.com/articles/static-sites-on-heroku

or you can use something like Octopress/Jekyll who uses sinatra.

But you need a minimum stack to serve html static content

Here is what worked for me:

cd myProject 
git init
heroku create myApp 
heroku git:remote -a myApp 

If the entry point is main.html, create index.php with this single line of content:

<?php include_once("main.html"); ?>

and then perform the following steps:

echo '{}' > composer.json 
git add . 
git commit -am "first commit" 
git push heroku master

Go to http://myApp.herokuapp.com/ and your app should be online now.

There's a much easier way to do it just in case anyone finds the other answers hard to follow.

Say you have your static website with the root at index.html. Now you want to deploy it to Heroku, how?

# initialise a git repo
git init

# add the files
git add -A

# commit the files
git commit -m "init commit"

# Now add two files at the root, composer.json and index.php
touch composer.json
touch index.php

# add this line to index.php, making a PHP app that simply displays index.html
<?php include_once("index.html"); ?>

# add an empty object to composer.json
{}

Now simply run git push heroku master and you're done!