Here is an idea you can try. Original table - no identity column table1 create a new table - call table2 along with identity column. copy the data from table1 to table2 - the identity column is populated automatically with auto incremented numbers.
rename the original table - table1 to table3 rename the new table - table2 to table1 (original table) Now you have the table1 with identity column included and populated for the existing data. after making sure there is no issue and working properly, drop the table3 when no longer needed.