Watermarking methods require robustness against various attacks. Conventional watermarking methods use error-correcting codes or spread spectrum to correct watermarking errors. Errors can also be reduced by embedding the watermark into the frequency domain and by using SIFT feature points. If the type and strength of the attack can be estimated, the errors can be further reduced. There are several types of attacks, such as scaling, rotation, and cropping, and it is necessary to aim for robustness against all of them. Focusing on the scaling tolerance of watermarks, we propose a watermarking method using SIFT feature points and DFT, and introduce a pilot signal. The proposed method estimates the scaling rate using the pilot signal in the form of a grid. When a stego-image is scaled, the grid interval of the pilot signal also changes, and the scaling rate can be estimated from the amount of change. The accuracy of estimating the scaling rate by the proposed method was evaluated in terms of the relative error of the scaling rate. The results show that the proposed method could reduce errors in the watermark by using the estimated scaling rate.