Redeploy Heroku app without code changes

Normally setting a config var causes your application to be restarted. In most situations there should be no need to redeploy after doing this.

If you really do need to trigger a new deployment you can add a new empty commit, then push to Heroku again:

git commit --allow-empty -m "Trigger Heroku deploy after enabling collectstatic"
git push heroku master

The new empty commit is a regular commit. It has a hash, an author, a timestamp, etc. It will have the same tree as its parent. This should cause Heroku to build your app slug again using the same code as the previous commit.

It's a bit awkward, but it works.

You can do it from UI as well!

1. Login to your Heroku dashboard and go to deploy section
2. Find Manual deploy option

Hit Deploy Branch button!

Note: you must have your app connected to GitHub for this option to be available (see comment from Derek below).