As a customer entity attribute, this field can be presented - and data can be captured - during checkout. If you want to convert it to a transactional record as part of the order, then that can be done as well, just as is done with other customer data at the time of order (remember, there is duplication of entity values relative to transactional moments, as this preserves historical info - think of a customer changing his or her name).
To find the implementation pattern, look at core markup & code which does this, e.g.
customer_firstname. This will lead you to Checkout and Sales modules, specifically to configuration values, setup scripts, etc.