This is the most complete version I could find:

READY FOR THE RIVER
Words by Gus Kahn, music by Neil Moret. ©1928.
As recorded by Annette Hanshaw, 1928-04-01

1. Tell the world that I'm all through with it.
No more will I moan.
Burn my home; what can I do with it?
Can't live all alone.
No use wastin' time.
I just know that I'm—

CHORUS 1: Ready for the river, the shivery river,
The river that goes down to the sea.
Want to drown my trouble, and leave just a bubble
To indicate what used to be me.
Made my will, wrote some notes.
Gonna keep a-walkin till my straw hat floats.
Said, I'm ready for the river, the shivery river,
So get that river ready for me.

2. Ain't no use to try to slow me down.
Can't stay; just can't stay.
{I don't know how you throw me down.
He's gone far away.}*
It was solitude.
That put me in this mood.

CHORUS 2: I'm ready for the river, the shivery river,
The river that goes down to the sea.
Want to drown my trouble, and leave just a bubble
To indicate what used to be me.
Make no fuss; make no row,
But I've just been two-timed for the last time now.
I'm ready for the river, the shivery river,
So get that river ready for me.

Deep river, my home is over Jordan.
Deep river, Lord, I want to cross over into camp.**

[Instrumental interlude]

Repeat verse 1.


* These lines are somewhat indistinct, and I think there must be something wrong with the way I transcribed them, because it seems awkward to have the pronoun switch from "you" to "he."

** An interpolation from an old spiritual.

Other early recordings were made by:
Emerson Gill and His Orchestra, 1928-03-27
Harold "Scrappy" Lambert, 1928-04-01
Wisconsin Roof Orchestra, 1928-05-01
Sam Lanin's Troubadors, 1928-05-10
Broadway Broadcasters (Lanin), 1928-05-10
Sam Lanin and His Orchestra, 1928-05-10
Coon Sanders Nighthawk Orchestra, 1928-05-29
The Goofus Five and Their Orchestra, 1928-06-27
Missouri Jazz Band, 1928-07-01