Aha. I'd incorrectly assumed that "round" was an informal coinage based on "around." Anyhow, first edition of the American Heritage gives "around" for the definition of "round" in its adverbial and prepositional form. And it doesn't qualify the word as "slang" or "informal," so no apostrophe would be needed even in American English. (But I'm not going to change my vote.)
The title of the Chuck Berry recording is "Around And Around"; the first time he comes up on it, he pronounces it "round 'n' around," the other times simply "round 'n' round." The Rolling Stones keep the American title but Mick sings it "round 'n' round." David Bowie, however, went all the way and spelled it "Round And Round."
Did the stand-alone phrase "I get around" ever exist in the UK?* I don't see how it could work as "I get round," though I do think "I'll get round to it" works fine. The "to it" makes us able to tell from context that you're not just getting chubby.
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The title of the Chuck Berry recording is "Around And Around"; the first time he comes up on it, he pronounces it "round 'n' around," the other times simply "round 'n' round." The Rolling Stones keep the American title but Mick sings it "round 'n' round." David Bowie, however, went all the way and spelled it "Round And Round."
Did the stand-alone phrase "I get around" ever exist in the UK?* I don't see how it could work as "I get round," though I do think "I'll get round to it" works fine. The "to it" makes us able to tell from context that you're not just getting chubby.
*Or "she sleeps around"?