Moving a local SQL Server database to Azure SQL Database is quite straight forward.
Pre-requisites: Before you move your local database, make sure you have created a Logical SQL Server on Azure already. Because we will be creating a copy of this local database on that Logical SQL Server.
Follow these simple steps:
Open SQL Server Management Studio, right-click on the database, select Tasks >> Deploy Database to Microsoft Azure SQL Database
Click on the Connect button to establish a server connection with your Azure Database.
Enter your Azure SQL Database Server Name, Login & Password in the popup window.
After the successful connection, select the Service Tier (Compute Size) and Storage Size for your database and then click Next. Refer to this link for more details - Service tiers in the DTU-based purchase model.
Wait for the operation to complete. This may take longer depending upon the size of the database.
That's all !!