Is there any medication/supplement that can help avoid recurrence of a base-of-tongue cancer?

No research based: Assuming you had appropriate therapy (surgery and/or radiation/chemo), close follow is the most important thing for you. There is no specific research I am aware of to recommend a specific supplement. A balanced diet, with lots of fruits and vegtables would be good, along with a multi-vitamin. Your pcp or oncologist may consider blood work to look for specific vitamin deficiencies like vit d.

No: There is no magic medicine or supplement. Though anti oxidant supplements have become big business. Adopt common sense advice by not drinking alcohol or smoke or chew tobacco. Eat healthy foods that are not over processed (in boxes and cans). Exercise regularly and keep a good weight for your height. Stay away from chemicals and toxic substances or at least be careful around these compounds.