I learned this version in Southern California in the early 60's:

I see the moon, the moon sees me,
down through the leaves of the old oak tree,
please let the light that shines on me, shine on the one I love.

Over the mountains, over the sea,
that's where my heart is longing to me,
please let the light that shines on me, shine on the one I love.

I kissed a rose, the rose kissed me.
fragrant as only a rose can be,
please let the light that shines on me, shine on the one I love.