Here is the tune as given in Roy Palmer's Songs of the Midlands (EP Publishing Ltd., 1972). It was noted by Cecil Sharp, from Priscilla Cooper, Stafford Common, Devonshire, 2 September 1902; and has here been altered by Pam Bishop to fit the broadside text, which is almost exactly as quoted above by Dan, with the additional verse quoted by Graham (though as usual, the word is my, not me).

X:1
T:American Stranger
S:Tune from Mrs. Priscilla Cooper, Stafford Common, Sept. 1902.
N:Noted by Cecil Sharp.
B:Songs of the Midlands, Roy Palmer, 1972.
Z:Tune modified by Pam Bishop.
L:1/8
Q:1/4=100
M:3/4
K:G
A A|d3 d c B|A2 G2 A A|B B G2 E2|D4
w:I'm a stran-ger in this coun-try from A-me-ri-ca I came.
A A|d2 e2 f2|e2 d2 (cB)|(AG) (EF) G2|A4
w:There is no-one that knows me nor_ can_ tell_ my name;
A A|d2 e2 f f|e2 d2 c B|A G (EF) G2|A4
w:I'm a stran-ger in this coun-try and shall tar-ry here_ a-while
A c|c2 A2 c B|(AG) E2 G2|A A G2 E2|D6|]
w:And I'll ram-ble from my dar-*ling for ma-ny a long mile.

Mrs. Cooper had what appeared to be an incomplete tune. Her text, rather different from the broadside given earlier (and muddled a bit with another song or two), was as follows:

I have been a-rambling by night and by day,
But to prove myself royals I will gang along with you;
I will take you to Amerikee, O my darling to be.

Some says I am ragged, some says I am poor,
But to prove myself royals I will gang along with you.

O in the middle of the ocean there shall grow a maypole tree
If ever I prove false to the girl that loves me.

Kind love to my Polly although she is poor,
Give my love to Betsy, she's the girl I adore.
I'll roll her in my arms on a cold winter's night.

And I wandered from my darling for many a long mile.
Now our ship it is ready, 'tis ready to set sail,
And I'll take you to Amerikee my darling to be.

But when we gets over to our own countree
We'll drink the good health to the Indian lass.


X:1
T:American Stranger
S:Mrs. Priscilla Cooper, Stafford Common, Sept. 1902.
N:Noted by Cecil Sharp.
B:Cecil Sharp's Collection of English Folk Songs, ed. Maud Karpeles, OUP, 1974.
L:1/8
Q:1/4=100
M:3/4
K:G
A2|d4 c2 B2 |A2 G4 A2| B2 G2 E2|D4
w:I have been a-ram-bling by night and by day,
AA|d2 e2 f2|e2 d4 cB|AG (EF) G2|A4
w:But to prove my-self ro-yals I will gang a-long_ with you;
Ac|d3 A CB|AG E2 GG |A2 G2 E2| D4|]
w:I will take you to A-me-ri-kee, O my dar-ling to be.

Text and tune both quoted from Cecil Sharp's Collection of English Folk Songs, ed. Maud Karpeles, OUP, 1974.