I want to use a slang term to make a sentence rhyme, but I want it known that I know how to spell it correctly.
Tennessee is where I
Let's consider some choices:
... where I wanna be
... where I *wanna be
... where I wanna [sic] be
Slang words are words. Just spell them the way you want them spelled. People are gonna either love it or hate it, and ya can't really help it. You can't really use a word and not use it at the same time; if using the word reflects badly on you then don't use it.
I don't know whether this will meet your purposes, but the only situation I know of where it is acceptable to misspell is when quoting someone else exactly. Publications do that, and if the quote contains an error, they include the word (sic) to show they know it is erroneous.
In the letter to parents it said: ‘The school is proud of it’s [sic] record of excellence’.
See if you can work with that.
There is no actual notation for slang that I know of. Quotation marks doesn't connotate the correct meaning. Quotations would suggest that you are being facetious and don't actually want to be in Tennessee. I would leave it as a regular part of your sentence.