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 our Developer page.
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, please contact our Support team by clicking on the purple chat icon in the bottom right corner of this page to start a chat.