In order to move local database to cloud SQL server you can use SysTools SQL to Azure Migration software. This program helps in migrating SQL Server database to Microsoft Azure SQL database. This tool also provides the functionality to migrate selective database objects to Azure.
Yes, there is a possibility of SQL database corruption when you move the database from local to the cloud. If a corruption occurs then, always restore the database from updated backup copy and if the backup is not available then, I will suggest checking this article: https://www.mssqltips.com/sqlservertip/6065/how-to-fix-sql-server-database-corruption-with-stellar-repair-for-ms-sql/
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