Now Azure Media Services adds support to manage resources through Azure Resources Manager (ARM). https://azure.microsoft.com/en-us/blog/azure-media-services-adds-support-to-manage-resources-through-azure-resources-manager-arm/ This means that you can deploy Azure Media Services with ARM template. You can deploy an new Azure Media Services account by simply clicking the following "Deploy to Azure" button.
See more details about the management API reference: https://msdn.microsoft.com/en-us/library/mt735160.aspx
-Shige