In order to leverage the Sitecore Publishing Service, you need the actual service and the module. The actual Publishing Service is what you will install to run the publishing as a distinct role, while the module is separate item added to your CMS and CDS roles.
The Publishing Service can be downloaded at: https://dev.sitecore.net/Downloads/Sitecore_Publishing_Service.aspx
Ensure you have the correct version by checking one of these two documents. The first is for older versions and the second, more current Publishing Services: https://kb.sitecore.net/articles/545289 or https://kb.sitecore.net/articles/761308
The modules can be found as a sublink in the Publishing Service page, or via the following if its Sitecore 9x: https://dev.sitecore.net/Downloads/Sitecore_Publishing_Service_Module.aspx
Make sure to download the instructions for both the Publishing Service or Publishing Service Module to ensure you are properly installing and configuring (and yes, you can run the Sitecore Publishing Service as an Azure Web App).