You can see the sheet music online at Indiana University Sheet Music Collections:

MEXICALI ROSE
Words, Helen Stone. Music, Jack B. Tenney.
Spanish translation by Manuel Sanchez De Lara.
Chicago : M. M. Cole Publishing Co., 1923.

1. Mexicali Rose, I'm leaving. Don't feel blue.
Mexicali Rose, stop grieving. I love you.
When the dove of love is winging through the blue,
All the castles you've been building will come true.

CHORUS: Mexicali Rose, stop crying.
I'll come back to you some sunny day.
Ev'ry night you'll know that I'll be pining,
Ev'ry hour a year while I'm away.
Dry those big brown eyes and smile, dear.
Banish all those tears and please don't sigh.
Kiss me once again and hold me.
Mexicali Rose, goodbye.

2. Mexicali Rose, I'll miss you when I go.
There'll be times I'll long to kiss you; that I know.
All the while I'll just be yearning, lonesome too,
Counting days till I'm returning, dear, to you.

Mexicali Rosa, Tengo que partir.
Mexicali Rosa, no debes sufrir.
En mis largas horas yo te estrañaré,
Y tus iluziones yo realizaré.

CHORUS: Mexicali Rosa no llores;
Piensa que muy pronto volveré,
Y que siempre triste sin Consuelo,
Cada non che y dia yo pasaré,
Seca tus hermossos ojos,
Deja de llorar y suspirar.
Besa me otra vez y es tré chame;
Mexicali Rosa adios.