Hello Frank Tricarico,
Currently that is not present functionality on the Links Widget. You can re-order items within the groups, but not the groups themselves.
We do have a Product Idea requesting this functionality. The ID for that idea is: CARE-I-38. You can vote for that idea by visiting: https://customercare.igloosoftware.com/support/product_zone and registering in the Product Idea portal.
Please let me know if you have any questions.