No – you have to do it the other way around: add it right from the get go as INT IDENTITY
– it will be filled with identity values when you do this:
ALTER TABLE dbo.YourTable
ADD ID INT IDENTITY
and then you can make it the primary key:
ALTER TABLE dbo.YourTable
ADD CONSTRAINT PK_YourTable
PRIMARY KEY(ID)
or if you prefer to do all in one step:
ALTER TABLE dbo.YourTable
ADD ID INT IDENTITY
CONSTRAINT PK_YourTable PRIMARY KEY CLUSTERED