'I'm rapt' is a peculiarly Australian expression, and its colloquial nature means that it doesn't often pop up in more formal writing contexts. However, when it does, using the 'rapt' spelling is preferable to writing 'I'm wrapped'.
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I've been musing on this point since spotting an article on Mumbrella yesterday which included a brief quote from radio personality Merrick Watts: "I'm rapt for them as a representative of the 'throw another steak on the barbie' campaign."
The spelling in that article is correct — but only because I sent in a comment and suggested the original copy, which used "wrapped", needed changing. It's an easy mistake to make, and Mumbrella fixed it very quickly.
The Macquarie Dictionary actually suggests that both spellings are equally acceptable. To my mind, using 'rapt' is definitely preferable, since it makes the connection to 'enraptured' rather more obvious. The sentences "I'm rapt for sex" and "I'm wrapped for sex" also have clearly different meanings.
Again, this isn't a phrase you'll use in highly formal contexts. However, even when writing informally, clarity counts.
Lifehacker's Mind Your Language column offers bossy advice on improving your writing.