I've heard David DeSilva and Ben Witherington III associated with the term "socio-rhetorical criticism" and Witherington even has a series of commentaries titled the "Socio-Rhetorical Commentary" series.
What is this form of criticism? Is it relatively new? Or is it a rebranding so-to-speak of the historical-grammatical method with simply a heavier focus on the cultural background? What does it hope to add to understanding the Bible?
I ordered his commentaries (Witherington) on Acts and Corinthians several years ago hoping there was some fresh perspectives of Greco-Roman culture. Basically what he tries to do is look at everything through a lens of Greek forms of rhetoric, showing how various arguments are not just imperical formulas under western ideas of induction and deduction, but rather in line with classical modes of pursuasion found among the Greeks and Romans.
Although this seems promising I have to say I can barely read more than five pages without feeling like a great backslide has occured even compared to Calvin's commentary on Acts. The insight is sadly lacking and the commentaries are not thourough verse by verse explanations but just platforms to propose a few average ideas with an attempt to show support for them by a section of scripture. What I mean is, he proposes some cultural idea to explain a key verse, which is often already moticed of in many old commentaries, then he half hazardly tosses a few more verses in the subseqent paragraphs to support his premise. In the meantime he almost ignores all the real meaty subjects that a true verse by verse commentary would typically cover.
In the end I would say it is all much ado about nothing. It is a fresh idea about sheding new light in a commentary that plays out to have little value in actually breaking new ground. I think he would have done better studying Jewish culture and looked at it through that lens, but that was probably not his major.
Actually, Vernon Robbins introduced socio-rhetorical interpretation into New Testament studies back in 1984, and Ben Witherington's more recent attempts to co-opt the term for what he does are much different. Robbins wrote a basic introduction to socio-rhetorical criticism back in 1996 (Exploring the Texture of Texts), but he has updated the approach in recent years. If you are looking for socio-rhetorical interpretation, Robbins and and the ones using a similar approach are the ones to read. You could also check my "Socio-rhetorical interpretation: Textures of a Text and its Reception in JSNT 33(2) 2010 191-206 or Robbins's Festschrift, Fabrics of Discourse. Sorry for the delay in answering; I just stumbled across the post accidentally while looking for something else.
