The tune became very well known not only in the United States but internationally; in 1841 the USA ambassador to Central America, John Lloyd Stephens, wrote that upon his arrival in Merida, Yucatan the local brass band played "Jump Jim Crow" under the mistaken impression that it was the USA's national anthem.
With time Jim Crow became a term often used to refer to African Americans, and from this the laws of racial segregation became known as Jim Crow laws.
The expression to jump Jim Crow came to mean "to act like a stereotyped stage caricature of a Negro". See Uncle Tom.
Here are the lyrics, from the band the Bluegrass Messengers, which has the song in its repetoire:
Come, listen, all you gals and boys, I'm just from Tuckyhoe;
I'm gwine to sing a little song, My name's Jim Crow.
Chorus: Wheel about, an' turn about, an' do jis so;
Eb'ry time I wheel about, I jump Jim Crow.
I went down to de river, I didn't mean to stay,
But there I see so many gals, I couldn't get away.
I'm rorer on de fiddle, an' down in ole Virginny,
Dey say I play de skientific, like massa Pagganninny.
I cut so many munky shines, I dance de galloppade;
An' w'en I done, I res' my head, on shubble, hoe or spade.
I met Miss Dina Scrub one day, I gib her sich a buss;
An' den she turn an' slap my face, an' make a mighty fuss.
De udder gals dey 'gin to fight, I tel'd dem wait a bit;
I'd hab dem all, jis one by one, as I tourt fit.
I wip de lion ob de west, I eat de alligator;
I put more water in my mouf, den boil ten load ob 'tator.
De way dey bake de hoe cake, Virginny nebber tire;
Dey put de doe upon de foot, an' stick 'em in de fire.