With SQL?

Two calls..
VB Code:
  1. CurrentDb.Execute "ALTER TABLE tablename ADD COLUMN NewField type NULL"
  2. CurrentDb.Execute "UPDATE tablename SET NewField=OldField"

Where type in the first SQL represents the field type that you are creating...

For more info try ALTER TABLE - SQL Command

Although this relates more to SQL Server it is possible to do this as a Hidden SQL option on Access