What a fabulous song! At youtube it's credited to Lebedeff and Alexander Olshanetsky, another Jew from Odessa, with publication date of 1926.
I put my translation of the Yiddish lyrics on the Youtube video of our very first performance of Vos ken you mach?:
But of course you HAVE to hear Lebedeff sing it, and luckily he's on youtube:
You can get the sheet music from me (with transliteration and translation of both verses) here:
You'll find this song under any combination of Yiddish and English words.
Vos is the Yiddish word for "what." You may also find "Vot."
Kenen is the Yiddish word for being able. So you can find "can" or "kan" or "ken."
You or "Yu" (this is not a Yiddish word)
Makhn is Yiddish for "make" or, here, "do." You can find "mach" or "makh"
S'iz is short for "es iz" (this is)
Amerike is the Yiddish word for America.
A klezmer singer from the Netherlands knew it under the title "Wot kann mann machen zis Amerike!"