“The voice is the voice of Jacob; the hands are the hands of Esau.” 
“Prayer is Israel’s only weapon, a weapon inherited from the fathers, tried in a thousand battles.”
I first saw this quotation in “Jewish Science: The Applied Psychology of Judaism,” citing only “Talmud” as its source. 
I believe that I later saw it in the Silverman (Conservative) machzor, with the same citation, but couldn’t locate it in preparing this article.
Some years ago, with the help of a librarian at Yeshiva University Library, I found: “Let others use their hands. Israel’s only weapon is prayer,” citing only “Yalkut” as a source. The librarian suggested that while there were several anthologies called “yalkut,” it can most often refer to “Yalkut Shimoni” (13th century midrashic anthology), as a midrash to Gen. 27:22.
“…inherited from the fathers, tried in a thousand battles” has a rather modern-prose sound to me. This might have been added later, but Rabbi Moses doesn’t cite in any greater detail the source from which he himself found the quotation. I’ve wondered whether Rabbi Silverman, who edited his machzor some years after Rabbi Moses wrote his own book, had borrowed from Rabbi Moses?
Another medieval midrash, Midrash Tanchuma  has the following:
“Your power [Israel] is stronger than his [Esau’s]. If Esau captures anyone…he is in [Esau’s] hand, but if that one flees, he can’t do a thing to him. With you [Israel], however, even though someone flees from one end of the world to another, ‘The voice is the voice of Jacob’ — You say something in the synagogue [i.e. in prayer] and…it comes to pass of its own accord.” 
Both “Shimoni” and “Tanchuma” interpret the “voice of Jacob” as Jacob’s voice heard in prayer. Judaism doesn’t advocate contemplative or silent prayer, although examples of it can be found. Instead, “prayer” usually means something uttered. The “Tefilah” — the Amidah or silent prayer that is said while standing — is the centerpiece of Jewish communal worship. But everywhere else, when the rabbis speak of “prayer,” they mean something audible, however barely. Rebbe Nachman’s “hitbodedut” is a another good example of this.
Thus, the “hands of Esau” is a metaphor for violent acts, while the “voice of Jacob” is a metaphor for prayer.
Yet, being medieval, even Yalkut Shimoni and Midrash Tanchuma are later collections of midrashim. Is there an earlier source?
Midrash Rabbah says:
“Jacob wields power only by his voice [i.e. in prayer; possibly meaning in audible Torah study as well]…Esau wields dominion only by his hands.” 
The Mekilta de-Rabbi Ishmael, another early rabbinic midrash, makes a similar point:
“Just as the worm has nothing to bring down the cedar with but its mouth, so Israel has nothing but prayer [i.e. which is done with his ‘mouth’).” 
The humble worm, using only its mouth, gradually brings down the mighty cedar. Just so, the rabbis are telling us, prayer can bring down even the most seemingly intractable obstacle. Not prayer, really; it is God who brings down the obstacle. Our prayer invites and allows God’s activity.
Thus, the idea that “Jacob’s voice” means “prayer,” and that prayer is Israel’s greatest tool, can be found in early rabbinic sources as well.
The rabbis are telling us that prayer itself is stronger than even the most seemingly overwhelming physical power. One need only think of the drowning of the Egyptians or the ultimate destruction of Nazi Germany — things that took place without an organized Jewish military force — for historical precedents. Where today is the Roman empire? Greek classical civilization? The Assyrian or Babylonian empires? Where is the Spanish empire that forced Jews out in 1492?
These are difficult times for the State of Israel and, increasingly, for Jews everywhere. Not to mention even worse times for many, many others.
Our own tradition tells us that prayer is our greatest defense. Not a prayer to destroy others. Rather — an affirmation that God is more real than the conditions that appear to us, and that even in the appearance of the worst conditions, God is producing Good that overwhelms all darkness and pain.
Real prayer is not a request. It is an act of creation.
Let Esau be Esau.
Let us be Israel.
 Ber./Gen. 27:22
 Moses, Rabbi Alfred Geiger; Jewish Science: The Applied Psychology of Judaism; © 1920 by Alfred G. Moses; p. 44
 par. 6:15 to Gen. 27:28, part VI
 Townsend, John T., trans.; Midrash Tanchuma; Ktav, © 1989; p. 160
 LXV: 20 to Gen. 27:22; Freedman, Rabbi Dr. H., trans.; Midrash Rabbah; © 1951 by Soncino Press; p. 595 (Genesis; vol. II)
 Lauterbach, Jacob Z.; Mekilta de-Rabbi Ishmael; © 1976 by Jewish Publication Society (paperback edition); vol. I, p. 207
[This is elsewhere translated: “Israel’s only weapon is prayer,” but this doesn’t strictly conform to the Hebrew. This quotation is followed by several aggadot — rabbinic stories — lauding the power of prayer.]