I had this issue where I had already created the table and could not change it without dropping the table so what I did was: (Not sure when they implemented this but had it in SQL 2016)
Right click on the table in the Object Explorer:
Script Table as > DROP And CREATE To > New Query Editor Window
Then do the edit to the script said by Josien; scroll to the bottom where the CREATE TABLE
is, find your Primary Key and append IDENTITY(1,1)
to the end before the comma. Run script.
The DROP and CREATE script was also helpful for me because of this issue. (Which the generated script handles.)