Who doesn't know this famous recruiting poster?
Now, I saw this very funny version in an English school:
Way to go students!
Hope you like it!
Um guia para quem estuda Inglês Online
It may be "headline" style: removing non-critical parts of speech for reasons of space and impact.
Headlines pack a great deal of information into a limited space, so it is not surprising that news headline writers use several methods to conserve space. One obvious example is to use abbreviations (“PM” for “Prime Minister”, etc.). But they also use a special grammar, omitting articles (“a” and “the”) and the verb “to be” wherever possible.
I think they mean 'I want you for Uncle Sam's army' and are then happy for it to turn into 'United States' Army' in the mind of the reader.
"I found several news stories in which the army was referred affectionately as "Uncle Sam's". For example, here is a headline from the New York Times of April 22, 1906.""General Corbin, the New Head of Uncle Sam's Army; How He Broke Up a Newspaper Establishment to Organize a Company in 1861 and Was Persuaded to Remain in the Army at the Close of the War by Grant."