OK, since what Peter Shor and I were telling you in the comments hasn't done the whole job, let's walk through this step by step:
- I'm goin'-a take that right hand road
"goin'-a" is an unusual way to write "gonna", which is a contraction of "going to" and yields
- I'm going to take that right hand road
"right hand" (or "right-hand") refers to something on the right side, which is experienced as the same side as your right hand. So "that right hand road" becomes "that road on the right side"
- I'm going to take that road on the right side.
Next, to "take" a road means to enter and travel along it:
- I'm going to go down that road on my right side
Now, if that's still not clear enough, let's paraphrase:
- I intend to take the road that branches off to my right side as I travel along in my present direction.
Not as artful as Mississippi Fred McDowell sings it, but perhaps clearer to someone who hasn't heard a lot of blues.
UPON FURTHER REVIEW: I was perhaps overlooking the religious overtones of the "right hand road" mentioned in the line. As WS2 and ab2 (who seem to have the same surname, "2") have suggested, the "right hand" in Christian gospel can refer to the "right hand of God" meaning the righteous path. That still needs to be understood through the filter of physical right vs. physical left, but it does add a religious dimension I didn't consider earlier. This is supported by the reference to the "river" (another bit of Christian symbology) and the direct address to the "Lord" (although such interjections occur even when there is no overt religious reference).