Companies that offer local numbers in your area may be able to port your existing landline fax number to their service.  Consult with their pre-sales or support pages with regards to availability.

Another option is to have your existing landline fax provider automatically forward incoming calls to your new internet fax number.  This is a great way to allow for a transitional period while people update their contact information with your new number, especially if you have just begun using a new toll-free fax number.