  In the framework of Soft-Collinear Effective Theory, the jet quenching
parameter, $\hat{q}$, has been evaluated by adding the effect of Glauber gluon
interactions to the propagation of a highly-energetic collinear parton in a
medium. The result, which holds in covariant gauges, has been expressed in
terms of the expectation value of two Wilson lines stretching along the
direction of the four-momentum of the parton. In this paper, we show how that
expression can be generalized to an arbitrary gauge by the addition of
transverse Wilson lines. The transverse Wilson lines are explicitly computed by
resumming interactions of the parton with Glauber gluons that appear only in
non-covariant gauges. As an application of our result, we discuss the
contribution to $\hat{q}$ coming from transverse momenta of order $g^2T$ in a
medium that is a weakly-coupled quark-gluon plasma.
