Hi, Pete - I've searched high and low, and I haven't found a Woody Guthrie recording of this song. Many other people recorded it, but not Woody. Cisco Houston's recording is probably the best-known rendition, followed perhaps by the recording by Judy Collins.
See the other threads on "Deportee": for a history of this song. Woody didn't write the tune - Joe Klein's Woody biography says he chanted the lyrics.
-Joe Offer-