Unfortunately if you just add an IDENTITY column to the table, the existing orders will not necessarily get the IDENTITY values assigned in order of the OrderDate, so they will be "out of order" if you wanted to assign order ID values based on order date (which seems logical). Quick example:
CREATE TABLE dbo.Orders
(
OrderGUID UNIQUEIDENTIFIER DEFAULT NEWID() PRIMARY KEY,
OrderDate DATETIME NOT NULL DEFAULT CURRENT_TIMESTAMP
);
INSERT dbo.Orders(OrderDate) VALUES
('20120101'), ('20120102'), ('20120103');
GO
ALTER TABLE dbo.Orders ADD OrderID INT IDENTITY(1,1);
GO
SELECT OrderID, OrderGUID, OrderDate = CONVERT(DATE, OrderDate)
FROM dbo.Orders
ORDER BY OrderDate;
Results (obviously yours will differ):
OrderID OrderGUID OrderDate
------- ------------------------------------ ----------
2 C5CE909E-0469-45AE-A828-647C7F54AA14 2012-01-01
1 70D8EEB1-FDA8-4E56-874F-771999C6DB84 2012-01-02
3 8E7B42C3-6C4D-4860-8A82-AFADDBA96A4A 2012-01-03
If this is not acceptable you should probably create a new table and insert all the old orders into it (at which point you can also drop the GUID column as I alluded to in my comment).
CREATE TABLE dbo.OrdersCopy
(
OrderID INT IDENTITY(1,1) PRIMARY KEY,
... other columns ...
);
INSERT dbo.OrdersCopy (OrderDate, ... other columns ...)
SELECT OrderDate, ... other columns ...
FROM dbo.Orders
ORDER BY OrderDate
OPTION (MAXDOP 1); -- single-threaded is important!
EXEC sp_rename 'dbo.Orders', 'OrdersOld', 'OBJECT';
EXEC sp_rename 'dbo.OrdersCopy', 'Orders', 'OBJECT';
(If you want to keep the old GUID for reference, temporarily, while you clean up other tables, that's probably fine, but you shouldn't make it auto-populate anymore, and you should plan to remove it since it's wide and redundant.)