Gravitational Faraday Rotation (GFR) is a frame-dragging effect induced by
rotating massive objects, which is one of the important, yet studied
characteristics of lensed gravitational waves (GWs). In this work, we calculate
the GFR angle $\chi_g$ of GWs in the weak deflection limit, assuming it is
lensed by a Kerr black hole (BH). We find that the GFR effect changes the
initial polarization state of the lensed GW. Compared with the Einstein
deflection angle, the dominant term of the rotation angle $\chi_g$ is a
second-order correction to the polarization angle, which depends on the
light-of-sight component of BH angular momentum. Such a rotation is tiny and
degenerates with the initial polarization angle. In some critical cases, the
GFR angle is close to the detection capability of the third-generation GW
detector network, although the degeneracy has to be broken.
