Although Winston has several guesses at Julia's age, we finally find out her true age in Part 2, Chapter 3. At that point, we are told explicitly that Julia is 26 years old. That is about what Winston had guessed.
Winston has been thinking about Julia in some way or other ever since we first meet her in Chapter 1. At that point he does not know her name, but she is described for us. At that point, she is described as "about 27." Later, when the two of them first meet and sleep together in Part 2, Chapter 2, Winston says that she is 10 to 15 years younger than his 39 years. Finally, in the next chapter when Winston is getting to know more about Julia, we are told she is 26.
As pointed out in the previous answer, Julia is in her mid-twenties, and therefore there is a not inconsiderable age-gap between her and Winston, who, we are told, is thirty-nine.
Julia's youthfulness is often emphasized in the novel. She is dark, pretty and attractive and Winston can hardly understand why she bothers with someone middle-aged and as unappealing as he feels himself to be. Also, he is an intellectual and she is not; she prefers to focus on her physical needs and desires. Certainly on the face of it they appear hardly compatible. Yet they are drawn together in their rebellion against the Party.
The unlikely pairing of Winston and Julia serves to highlight how even the most disparate of individuals can be united in a common cause against the most diabolical type of oppression. The Party seeks to strictly regiment all of its members, but underneath a façade of outward conformity, Julia and Winston are highly individualized characters.