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.

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