This is how you add an existing user to a SQL Server (or Azure SQL) database via TSQL:
Prerequisites: The login
My_User already exists in the SQL Server.
Step 1 - Connect to the correct database
Step 2 - Create the user:
CREATE USER My_User FOR LOGIN My_User;
Steg 3 - Grant the user access
EXEC sp_addrolemember N'db_owner', N'My_User'
Note: give the user as litte access as possible. You can read more about SQL Server datbase-level roles here.