How can I search for a commit message on GitHub?

You used to be able to do this, but GitHub removed this feature at some point mid-2013. To achieve this locally, you can do:

git log -g --grep=STRING

(Use the -g flag if you want to search other branches and dangling commits.)

-g, --walk-reflogs
    Instead of walking the commit ancestry chain, walk reflog entries from
    the most recent one to older ones.

Update (2017/01/05):

GitHub has published an update that allows you now to search within commit messages from within their UI. See blog post for more information.

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I had the same question and contacted someone GitHub yesterday:

Since they switched their search engine to Elasticsearch it's not possible to search for commit messages using the GitHub UI. But that feature is on the team's wishlist.

Unfortunately there's no release date for that function right now.