FORTUNE — At a bar in Brooklyn not long ago, this author pointed to a bottle of Tito’s Handmade Vodka on the shelf, and asked if it was any good. The bartender, a Tito’s fan, was eager to pour a sample. A neighboring patron chimed in that she has loved the drink for years.

Tito’s is still a small brand, and if it doesn’t exactly have mainstream appeal yet, it’s getting there fast. Thanks in part to enthusiastic bartenders like Tony Abou-Ganimin in Las Vegas, its growth in recent years from its start in 1997 has been explosive. In 2010 it sold 365,000 cases. Last year, it sold 850,000 cases, according to Impact Databank, which tracks industry sales. For comparison, Skyy Vodka sold 2.9 million cases. Tito’s, which competes in the premium vodka market, typically retails for about $25 for a one liter bottle in the U.S.

That growth is an especially impressive feat considering that, like most vodkas, Tito’s defining characteristic might be that it has no defining characteristics, though devotees swear by its smooth finish. What it does have is an endearingly simple label (the founder, Tito, designed it himself), a good founding story, and even better timing — Tito’s started ramping up production just as the craze for craft brewing gripped the nation.

“There’s a lot of discovery involved,” says David Fleming, executive editor of beverage trade magazine Impact. “It’s countercultural, and people like to brand themselves with something that isn’t already well known.” Tito’s craft credibility may be fading now that the distiller is producing hundreds of thousands cases a year, but it’s still a long way from having the staid corporate sheen of the major players.

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Its ambitions don’t stop here, though. This year, the distiller aims to parlay its stateside success into a global brand. Tito’s is launching its first international expansion this quarter, with plans to sell the drink in countries including the UK, New Zealand, Singapore, Thailand and Mexico. It’s aiming high: “This brand is going to totally disrupt the vodka category outside the U.S.,” claims Tito’s new international sales chief John McDonnell.

But compared to whiskey, American vodka — even an industry darling — will be a tough sell overseas.

As Fortune reported in a recent cover story, American whiskey exports have soared in recent years, nearly tripling over the last decade to $1 billion last year. American spirits overall topped a record $1.5 billion in exports. Global trends are in their favor. Though an international thirst for American products isn’t new (bonjour, Levis), there’s a growing enthusiasm for specialty cocktails, which continue to gain vs. wine or beer.

Vodka, notably, has been absent from the party. Even though Americans drink more of it than any other distilled spirit (it accounts for about a third of overall sales), last year the relatively tiny U.S. vodka industry exported just $54 million worth of booze — about one-twentieth of whiskey exports, according to the Distilled Spirits Council of the United States.

The economics are tough. Globally, people drink more vodka, but spend less on it. Paying premium prices for the mostly tasteless liquor is uniquely an American phenomenon. It started in the 80s with the rise of Absolut. “In marketing speak almost overnight America became this upscale vodka market in a really big way,” says Impact’s Fleming. “You really only see that here.” Overseas? “I would kind of compare it to the Champagne business in the region of Champagne,” he says. “People drink Champagne every day. It’s not considered high end.”

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To help break into those global markets, Tito’s has brought in some big guns. It hired John McDonnell, formerly the COO of Patron Spirits International. McDonnell, who will spearhead Tito’s international expansion, worked for Patron for eight years and is credited with helping to propel the domestic tequila brand from 340,000 cases per year to a 2-million case global powerhouse.

McDonnell thinks that global enthusiasm for Americana will buoy Tito’s, as will being the first handcrafted U.S. vodka sold overseas. Despite its growth, the company still uses its original distillation process: copper pot stills and a 100% corn base. As for marketing, Tito’s will rely on the same homespun story that launched it to prominence in the U.S. That message hinges on the authenticity of its founder, Bert “Bertito” Beveridge. Beveridge started the company in 1997, battling Texas regulatory authorities to set up the distillery. Bucking the industry trend, the company doesn’t do flavors and the label is barebones. Or as McDonnell says: “No frosting necessary.” If that weren’t enough, Tito’s also adopts rescue dogs. The distillery has found homes for 32 dogs, two of which live full-time at the distillery. Beveridge says he has no plans to sell the company, saying via e-mail, “It’s more fun to be Tito who owns Tito’s than to be Tito who used to own Tito’s.”

Overseas, the drink’s rustic American branding will stay pretty much the same. “It’s a global message,” says McDonnell, “and we’re going to stick with the story that got us to the party.”

Beveridge says he’s undeterred by the vodka-soaked global markets in his quest for international expansion. He writes that his vision for the company is for people to be able to “enjoy Tito’s Handmade Vodka just about anywhere in the world,” yet the company recognizes its shtick may have its limits. “It’s a tall order trying to sell vodka to Russians and Poles,” McDonnell says. “But there are a couple of hundred other countries that I can go to before them.”