Many rocks exhibit transversely isotropic (TI) characteristics. For determining the TI property using acoustic logging, Stoneley waves are the only borehole wave mode that has a significant sensitivity to TI effects, especially when the formation is acoustically slow compared to the borehole fluid. This study describes a method for deriving the formation shear-wave TI parameter from the Stoneley wave data acquired by a logging tool. It is shown that the presence of the tool in the borehole can substantially affect the Stoneley wave propagation. Fortunately, for low-frequency Stoneley waves, the tool effect can be satisfactorily modeled using an effective modulus, regardless of the actual structure of the tool. The modulus can be determined from a calibration procedure. In the inversion processing of the Stoneley wave data, the Stoneley wave slowness is related to the weighted average of the wave's dispersion curve over the frequency range occupied by the wave spectrum. This provides a fast method for the inversion. As a processing example, this method has been applied to estimate the shear-wave TI parameter profile for the Lewis shale formation in Braggs, Wyoming. The resulting profile delineates the shear-wave anisotropy magnitude and variation for this shale formation.