After all, the United States was once part of the British Empire. If, for some reason, there was a groundswell of support among U.S. citizens and leaders for entry into the Commonwealth, could we join?
Sounds extremely unlikely. Why would the US want to join? It’s not exactly the world’s most task-driven institution, so far as I can see. Still…
The US would have to recognize the Queen as “head of the Commonwealth”, IIRC, which might prove a sticking point.
Also, I doubt other members would want the US there.
(Maybe that’s why the Commonwealth exists - somewhere to get away from the Americans. Best explanation I’ve ever heard 
)
Sure - the membership requirements are here.
All members except Mozambique have been under British rule. Current rules state that to join
So, the US would qualify easily. There are already 1.7 billion people in the Commonwealth, so I’m sure we could find room for you. You’d have to promise not to go winning all the medals at the Commonwealth Games, though.
Let the Americans in to our club?
Sorry, no tie? no jacket? no service!
We have to have some standards you know.
Hmmm, perhaps…
We may have a vacancy coming up, as long as you book early enough. We’ll seat you where Zimbabwe used to sit.
This question was asked a year or so ago.
To sum up, the U.S. could join, but there is really no good reason for it do so. The U.S. doesn’t really need to join a political union which it isn’t the head of.
We Americans have this thing about being in charge.
And even though the Queen has no power over the Commonwealth, most of the US would freak over being associated with royalty.
We like to gossip about the royals, but we don’t want to be ruled by them.
Except for the few remaining members of the Federalist Party.
Well they would have to pay the back taxes on the tea first. 
By far the best and most reasonable answer, yet! 
I think a better idea would be to expand NAFTA to include Commonwealth members. I believe Britain is considering this already?
I think a trading block among the planet’s English-speaking nations would be another possibility.
Trading block and military alliance. We might as well formalize a relationship that, for all intents & purposes, exists anyway.
Great answers, all. Thanks for satisfying my curiosity.
I think we can be frank about this - the above is true. But we love you Yanks, we really do. Think of the Commonwealth, not so much as an anti-American institution, but as a kind of non-American chill out room for the rest of us. I have enough faith in my American friends that they’d be cool enough with this idea. Sometimes we just need a little space to check the cricket scores, drink some decent beer, whack a few superfluous "U"s in our nouns, and listen to the Goon Show. Nothing personal old chaps.