Currently, there are two distinct ways to access AGROVOC data without the need of a UI:

SPARQL endpoint

https://agrovoc.fao.org/sparql

Skosmos REST APIs

Skosmos  provides a set of REST APIs to access its vocabulary data. The official AGROVOC Skosmos deployment can be accessed here. Using this REST APIs, it is possible, among other things, to search for concepts through its labels, filters such searches using specific languages (in the search term or even in the returned data) and then get all the information of a given concept.

Here are a couple of examples on these REST APIs:

Search all concepts having a label in English (en) starting with the word “bea”: 
https://agrovoc.fao.org/browse/rest/v1/search/?query=bea*&lang=en

Search all concepts having a label in English (en) containing the word “bea”: 
https://agrovoc.fao.org/browse/rest/v1/search/?query=*bea*&lang=en

Getting all data associated to the concept 
http://aims.fao.org/aos/agrovoc/c_3077 : https://agrovoc.fao.org/browse/rest/v1/data/?uri=http://aims.fao.org/aos/agrovoc/c_3077

To have the complete list of REST APIs available, please refer to the official guide.