C F A# D# G C according to the tab on here. idk how accurate that is, though
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If that's not right try 'Spanish tuning' also called open G tuning. It was used by a lot of delta blues players but I'm not sure about that specific song. Tuning is DGDGBD.
Judging from this youtube...

... it's B-E-A-D-F#-B. That's standard tuning 5 half-steps down.
I was common to tune a 12-string guitar down 4 or 5 half-steps. Blind Willie McTell tuned his down 4 half-steps (C-F-Bb-Eb-G-C), and this Leadbelly tune could be the same (as in the tab) if the original recording has been sped up a little.

He's playing in "E" btw (ie.. concert B major, played as E shape), and improvising around the open position chord shape.