Query: "A high tuck a-haw" in "Turkey in the Straw"

[Gerald Cohen]

A colleague has asked me about the meaning of "A high tuck-a-haw" in
the lyrics of the song "Turkey in the Straw."  Would anyone know?
The relevant verse is:

        Turkey in the straw,
        Turkey in the straw,
        Roll 'em up and twist 'em up
        A high tuck a-haw
        And hit 'em up a tune called
        Turkey in the Straw.

Also, what does "Roll 'em up and twist 'em up" refer to?

Gerald Cohen