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Yes, you can use the REST API to query workbooks.
You may also want to explore Postman and a Tableau Collection as a way to learn about the API's. When/if you need to do anything further programmatically with our API's, I highly recommend Tableau_Tools which is a wrapper around the API and obfuscates many of the administrative parts of building an application.
Are you after the URL of the Workbook, or the URL of a view within a workbook?