It's in Edward Arthur Dolph, Sound Off!: Soldier Songs from Yankee Doodle to Parley Voo (Cosmopolitan Book Corporation, 1929, pp. 552-54). Tempo is Allegretto. Text (without tune) is quoted from Dolph's book in Lingenfelter & Dwyer's Songs of the American West (p. 292).

X:1
T:OLD ARIZONA AGAIN
T:(Old Fourth Cavalry Song)
M:6/8
L:1/8
B:Dolph, Sound Off! 1929 pp. 552-54
K:Eb
E/ E/|G G G F E D|C3-C2 E|
w:Oh, it's old Ar-i-zo-na a-gain,_ It's
G G G F E D|C3-C2 G/ G/||
w:old Ar-i-zo-na a-gain;_ It's a
M:C
c2 c c =B2 =A2|G6 G G|
w:place where we all have been. We have
=A A A A Hc2 F F|
w:all been there be-fore, And we're
G G G G Hc2 E E||
w:go-ing back once more, Back to
M:6/8
G G G F E D|C3-C2|]
w:old Ar-i-zo-na a-gain._

Oh, it's old Arizona again,
It's old Arizona again;
It's a place where we all have been.
We have all been there before,
And we're going back once more,
Back to old Arizona again.

Oh, it's old Arizona again,
It's old Arizona again;
With its greasers and bad, bad men.
They dom't know the Boston dip
But they shoot you from the hip
Down in old Arizona again.

Oh, it's old Arizona again,
It's old Arizona again;
It's a place where we all have been.
With its scenery and fresh air,
They will be your bill of fare,
Down in old Arizona again.

Oh, it's old Arizona again,
It's old Arizona again;
It's a place where we all have been.
With the bears and rocky ground,
And the rattlers running round,
Round in old Arizona again.

Oh, it's old Arizona again,
It's old Arizona again;
It's a place where we all have been.
And if you get away,
They will bring you back to stay,
Down in old Arizona again.