I parse it as "Is there [a man] that for honest poverty hangs his head", with "that" displaced for rhythm's sake. I admit that that is pretty far-fetched, tho, and I cannot think of another instance of the part of the construction that amounts to the suppression of the subject of "there is".

For further perplexity, note the curious punctuation of the original:

Is there, for honest Poverty
    That hings his head, and a' that;

(_Burns: Poems and Songs_, ed. by James Kinsley, Oxford U.P., 1969)