Surprised that this on isn't listed in the Spirituals Permathread (38686). There are two fairly modern versions in the DT.
The Cleveland Index lists this spiritual in Burlin, Dann, Dett, Fenner, Fisher (as "Let My People Go"), Frey, Grey, Johnson, Jubilee and Plantation songs, White, and Weir.
The Nineteenth Century is the earliest recorded occurrence. Here is the 1872 version as sung by the Jubilee Singers, Fisk Institute.

Lyr. Add: GO DOWN MOSES
^^
When Israel was in Egypt's land;
Let my people go,
Opressed so hard they could not stand,
Let my people go.

Chorus:
Go down, Moses, way down in Egypt's land.
Tell old Pharoah, Let my people go.

Thus saith the Lord, bold Moses said,
Let my people go;
If not I'll smite your first-born dead,
Let my people go.

No more shall they in bondage toil,
Let my people go;
Let them come out with Egypt's spoil,
Let my people go.

When Israel out of Egypt came,
Let my people go;
And left the proud opressive land,
Let my people go.

O. 'twas a dark and dismal night,
Let my people go;
When Moses led the Israelites,
Let my people go.

'Twas good old Moses and Aaron too,
Let my people go;
'Twas they that led the armies through,
Let my people go.

The Lord told Moses what to do,
Let my people go;
To lead the children of Israel through,
Let my people go.

O come along Moses, you'll not get lost,
Let my people go;
Stretch out your rod and come across,
Let my people go.

When they reached the other shore,
Let my people go;
They sang a song of triumph o'er,
Let my people go.

Pharoah said he would go across,
Let my people go;
But Pharoh and his host were lost,
Let my people go.

O Moses the cloud shall cleve the way,
Let my people go;
A fire by night, a shade by day,
Let my people go.

You'll not get lost in the wilderness,
Let my people go;
With a lighted candle in your breast,
Let my people go.

Jordan shall stand up like a wall,
Let my people go;
And the walls of Jerico shall fall,
Let my people go.

Your foes shall not before you stand,
Let my people go;
And you'll possess fair Canaan's land,
Let my people go.

'Twas just about in harvest time,
Let my people go;
When Joshus led his host divine,
Let my people go.

O let us all from bondage flee,
Let my people go;
And let us all in Christ be free,
Let my people go.

We need not always weep and moan,
Let my people go;
And wear these slavery chains forlorn,
Let my people go.

This world's a wilderness of woe,
Let my people go;
O, let us on to Canaan go,
Let my people go.

What a beautiful morning that will be,
Let my people go;
When time breaks up in eternity,
Let my people go.

The Devil he thought he had me fast,
Let my people go;
But I thought I'd break his chains at last,
Let my people go.

O take yer shoes off yer feet,
Let my people go;
And walk into the golden street,
Let my people go.

I'll tell you what I likes de best,
Let my people go;
It is the shouting Methodist,
Let my people go.

I do believe without a doubt,
Let my people go;
That a Christian has the right to shout,
Let my people go.

Source: [Seward, T. F., compiler] "Jubilee Songs: As Sung by the Jubilee Singers of Fisk University, Nashville, Tenn., under the auspices of the American Missionary Association." New York: Biglow and Main, c. 1872, pp. 22-23. Reproduced in "Sinful Tunes and Spirituals, Black Folk Music to the Civil War," Dena J. Epstein, pp. 372-373 (Song of the Contrabandists also reproduced).