I'm not sure if his age was ever made clear. I think there is a spin-off about him, but I'm not so sure as to how it relates to the main narrative.
How old is Han Tzu, aka "Hot Soup", in Ender's Game?
Inspired by this question: How old is Finn?.
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His age is never directly stated, but inferences can be made.
Han Tzu was a toon leader in Drgaon Army under Ender:
Han Tzu, commonly called Hot Soup, was the leader of D toon. He slid quickly along the lip of the star to where Ender knelt. "How about flipping off the north wall and kneeling on their faces?" (Ender's Game, chapter 11)
Ender's Toon leaders were veterans beforehand:
His ragged little group of veterans, utterly without honor in their previous armies, were blossoming into capable leaders. So much so that instead of the usual four toons, he had created five, each with a toon leader and a second; every veteran had a position. (Ender's Game, chapter 11)
His veterans were all younger than Ender, with under 1 1/2 years in the Battle Room:
Not one of the veterans belonged to Ender's elite practice group. None had ever been a toon leader. None, in fact, was older than Ender himself, which meant that even his veterans didn't have more than eighteen months' experience. Some he didn't even recognize, they had made so little impression. (Ender's Game, chapter 10)
Ender was nine and a half at the time:
Young as he is. we've never had a boy better prepared for command. Usually they go at eleven. but at nine and a half he's top flight." (Ender's Game, chapter 10)
And people (besides for Ender) didn't get promoted until age eight:
Ender shook his head. It was the stupidest thing he could think of, to promote him now. Nobody got promoted before they were eight years old. (Ender's Game, chapter 7)
This puts an upper limit on his age as being Ender's age (6 1/2 at the beginning of the book), and a lower limit of being 8 at the time (5 at the beginning of the book).
As Praxis pointed out, we know from Cheater that he took the Battle School test at age five:
We want you to be one of the best of all the five-year-old children in the world. (Cheater)
But not knowing when this story is set in relation to Ender's Game makes it of little use.
So I would put his age as being between 5 and 6 1/2 when the book starts.
The richest source of detail concerning Han Tzu is Orson Scott Card's short story "Cheater", which first appeared in his InterGalactic Medicine Show e-zine. The story expores Han Tzu's back story just prior to Ender's Game. (This is probably the "spin-off" you are referring to.)
I've read the whole story and it doesn't give his age (or the age at which he is drafted into Battle School), only mentioning that he was older than 5 at the time of the events in question, and so I assume he is between 5 and 6 at that time, Even if it gave an exact age, it would be difficult to extrapolate a "current" age without knowing more details.