I found this version at http://www.traditionalmusic.co.uk. It's taken from Wehman's Universal Songster - complete collection of 61 volumes (Volume 32). It includes an additional verse about the stepmother singing a song the mother used to sing, and I think that makes the lyrics feel more complete.

I CANNOT CALL HER MOTHER.

The marriage rite is over; and though I turn aside.
To keep the guests from seeing the tears I could not hide,
I wreathed my face in smiling, and led my little brother
To greet my father's chosen-but I could not call her mother.

She is a fair young creature, with meek and gentle air;
With blue eyes soft and loving, And silken, sunny hair.
I know my father gives her the love he bore another;
But, if she were an angel, I could not call her mother.

To-night I heard her singing a song I used to love,
When its sweet notes were uttered by her who sings above;
It pained my heart to hear it, for my tears I could not smother,
For every word was hallowed by the dear voice of my mother.

My father, in the sunshine of happy days to come.
May half forget the shadow that darkened our old home.
His heart no more is lonely; but me and little brother
Must still be orphan children-God can give us but one mother.

---

Click here for three versions from Randolph.

There's another melody in a book titled Singing in Zion.