Here's another version with slightly stronger language (coyly hidden in 18th century style by missing out letters), from James Barke and Sydney Goodsir Smith's 1965 edition of The Merry Muses of Caledonia, originally printed in 1800. Judging by what's on YouTube, it looks as if this version is the one preferred by singers nowadays. As Joe says, attribution to Burns can't be proved, but a number of scholars seem to have considered it likely to be his work.

WHA'LL MOW ME NOW?
TUNE: Comin' thro' the rye

O, I hae tint my rosy cheek,
Likewise my waste sae sma';
O wae gae by the sodger lown,
The sodger did it a'.

O Wha'll m-w me now, my jo,
An' wha'll m-w me now:
A sodger wi' his bandileers
Has bang'd my belly fu'.

Now I maun thole the scornfu' sneer
O' mony a' saucy quine;
When, curse upon her godly face!
Her c--t's as merry's mine.

Our dame hauds up her wanton tail,
As due as she gaes lie;
An' yet misca's [a] young thing,
The trade if she but try.

Our dame can lae her ain gudeman,
An' m-w for glutton greed;
An' yet misca's a poor thing
That's m--n' for its bread.

Alake! sae sweet a tree as love,
Sic bitter fruit should bear!
Alake, that e'er a merry a--e,
Should draw a sa'tty tear.

But deevil damn the lousy loon,
Denies the bairn he got!
Or lea's the merry a--e he lo'ed
To wear a ragged coat!