Both of these suggestions are about the only ways to go.
One small advantage of PCJock's suggestion (a new column) is that the table permissions aren't affected. When going with the 'new table' approach, permissions would have to be re-applied to the new table.
Also, with PCJock's suggestion, if the identity column is the PK in that table, then you'll probably want to make some other column the PK (perhaps the new non-identity column?)
If there are other tables with FK constraints to your table, then you won't be able to delete the table unless you first remove the constraints.