You can use a plugin heroku push that is built by one of the Heroku engineers. You can find it at https://github.com/ddollar/heroku-push. But there isn’t a FTP style upload available if that’s what you’re looking for.
Also, just because Heroku uses Git doesn’t mean you have to have a Github account (since you mention having to have a premium account). All Github provides is an additional place to store your code if you are working on it in a team. There is absolutely NO REASON that you have to use github to use Heroku.
UPDATE: Heroku recently introduced programmatic builds which let you deploy a TAR file directly to Heroku via their API. Read more at https://blog.heroku.com/archives/2013/12/20/programmatically_release_code_to_heroku_using_the_platform_api
UPDATE2: Heroku have now introduced HTTP GIT – much simpler without having to deal with SSH keys and such like. Also, DropBox deployment is pretty neat.