An international language will always struggle to express purely national concepts - and regional foods and beverages fall strongly into this category. Root Beer is very much an American phenomenon and has not been widely exported like cola and fanta have been. Consequently, one should not expect Esperanto to have a good expression for this - certainly not one that will resonate with anybody not familiar with American culture and the English language.

You'll find suggestions in bilingual dictionaries such as radikbiero or sasafrasaĵo, but use them with caution - and be prepared to explain what they're supposed to mean. (Maybe even include the regional name "root beer.")

I also found these links useful:

Kiel traduki "root beer"? http://www.argilo.net/node/73

Kiel traduki "root beer"? http://argilo.livejournal.com/10203.html?thread=16347