Can I install SQL Server Management Studio on Windows ARM64-based?
I don't see why not
SQL Server Management Studio should support all new versions of windows and it is support 64bit
You can get the list of SSMS System Requirements in this document:
In the same document you have the link to download the application
With that said, you can always try to use Azure Data Studio first. The Azure Data Studio can be used without any installation even from external disk-on-key for example. Moreover, it is open source and free and has version for all common operating systems.