“Stop Stop Stop” by the Hollies:
Then, of course, the singer gets kicked out of the club for getting handsy.
Does Walk the Moon’s “Shut Up and Dance with Me” count?
And if non-English songs count, Yvette Giraud’s “La danseuse est creole”.
The long Gotta Dance sequence from Singin’ In The Rain.
And before anyone says it’s about dancing, it’s the story of a guy seeking employment as a professional dancer
Harvest Moon, Neil Young
“I’m 'n Luv (Wit a Stripper)” by T-Pain
“Ten Cents A Dance”
Thirty posts, and no one has mentioned “Cheek to Cheek”? :eek:
*Heaven, I’m in Heaven
And my heart beats so that I can hardly speak;
And I seem to find the happiness I seek
When we’re out together dancing, cheek to cheek
Heaven, I’m in Heaven
And the cares that hung around me thru the week
Seem to vanish like a gambler’s lucky streak
When we’re out together dancing, cheek to cheek*
Old 97s - “The Dance Class”. The protagonist is an agoraphobe in love with a girl in a dance class across the street.
“I’m wishing I could leave my house
But it’s been a year since I went out
You’re so far over there in your dance class
I am in love with whoever you are
Whoever you are…”
Presumably because it’s about dancing rather than specifically about a dancer as the OP requested. See posts #5 and 8.
It’s Fred Astaire singing about himself dancing with Ginger Rogers as he dances with Ginger Rogers. How does this not meet the criteria? 
Tomorrow from Bugsy Malone. Technically about someone that *wants *to be a professional dancer.
Kinks, “Come Dancing”
Specifically about Ray Davies’ sister (who, in real life, died of a heart condition in a dance hall)
Well, take it up with the OP, but ISTM that it’s pretty clear that the OP’s criterion is a description of someone else dancing. Not about the emotions that the experience of dancing makes the narrator feel (which is what “Cheek to Cheek” is about), even if the singer happens to be a famous dancer in real life.
For example, the OP explicitly disqualified “The Safety Dance”, which is also about the narrator’s feelings about dancing.
Jackson Browne - For a Dancer
I realize that all songs about dancing are also about the people doing the dancing, but for the purpose of this thread I would just like to stick to songs about the dancers themselves.
Would Copacabana count? Lola is a dancer, but most of the plot of the song is about stuff to the side of that (a couple men fighting over her, her being a has-been who’s still trying to cling to when she was Hot Stuff)…though it is all consequences of her dancing.