Did Gravity Probe B provide any bounds on Einstein-Cartan torsion? is a non-zero torsion value at odds with the results regarding frame-dragging and geodetic effects?
There is a Phys Rev D paper from 2007 ("Constraining torsion with Gravity Probe B", by Mao, Tegmark, Guth and Cabi, gr-qc:0608121) which discusses testing torsion using Gravity Probe B, and provides bounds on some parameters given the preliminary data available at the time. A more recent PhD thesis by one of the authors contains a somewhat updated version, see arXiv:0808.2063. However, there is another paper by Flanagan and Rosenthal (arxiv:07041447) which appears to show that theories of the form discussed in these other papers are only internally consistent for ranges of parameters which do not produce effects detectable by Gravity Probe B.
Looking through the papers citing these papers, there appears to be no updated analysis with respect to bounds on torsion. That said, this is far from my area of expertise, so perhaps someone else can give you an authoritative answer.
Like Joe, this isn't my area of expertise, but there are some more recent papers that I know of. Another Phys. Rev. D paper from Feb. 2011 (Constraining spacetime torsion with the Moon and Mercury, arxiv:1101.2789v2) has been on my computer for a couple months, but I haven't looked at it yet. The same authors wrote a July 2011 paper (Constraining spacetime torsion with LAGEOS, arXiv:1101.2791v3), which I know even less about than the previous one. A basic overview of the group's work is available here, and it appears that some more results may be forthcoming. As I haven't read any of the papers seriously, I can't personally speak for their accuracy.