refer an enumerator value with specified index

You could use take to peel off the first three elements and then last to grab the third element from the array that take gives you:

third = enum.take(3).last

If you don't want to generate any arrays at all then perhaps:

# If enum isn't an Enumerator then 'enum = enum.to_enum' or 'enum = enum.each'
# to make it one.
(3 - 1).times { enum.next }
third = enum.next

Alternative to mu's answer using enumerable-lazy or Ruby 2.1. As lazy as using next but much more declarative:

enum.lazy.drop(2).first