In order to add a primary key to an existing table we need to use the Alter Table command.
Add a primary key for a new column
ALTER TABLE dbo.Presidents ADD PresidentID int NOT NULL IDENTITY(1,1) CONSTRAINT PK_PresidentID PRIMARY KEY NONCLUSTERED
Note however that the ordering of the identity field will not be predictable for the records that already exist in the table. For newly inserted records, the identity field will increment properly.
Add a primary key for an existing column
ALTER TABLE dbo.Presidents WITH NOCHECK ADD CONSTRAINT PK_PresidentNumber PRIMARY KEY NONCLUSTERED (PresidentNumber)
