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.

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