I am migrating my Database to SQL Azure. Everything is working fine except scheduling Full-Text Catalog. I am somehow not able to schedule the Catalog.
I know we can use Scheduler but is there somehow anyway that I can directly schedule it directly through Azure SQL Database?
There is not an option to do Scheduling directly in Azure SQL Database. However, as you seem to imply, there are ways to do this with Azure offerings- see Elastic Jobs, which is designed for scaling administrative tasks but also has a scheduling component.