Yes, we do! All Toggl Track users are welcome to use the public API to create their own Toggl Track implementations. Using the API doesn't require a paid plan. Detailed API documentation is available on GitHub.
Along with the API, you're welcome to contribute to Toggl Track's open-source projects. We will review your contribution and merge it with master if it meets our standards.
Open-source Toggl Track clients
Toggl Track also supports webhooks, more here.
If you need any more information about our API, you can contact our support team via email. :)