(Consolidating two answers given in comments as a Community Wiki answer)

First of all, there's JGit:

JGit is an EDL (new-style BSD) licensed, lightweight, pure Java library implementing the Git version control system.

And then there's the Stash Java Client:

The Stash Java Client, is a small, light-weight Java library that can be used to interface with a Stash instance via its REST API.