The traditional speckle correlation method has a range limit in the angular displacement measurement of structural members. Aiming at this problem, a speckle correlation method for the angular displacement measurement by using log-polar transformation is presented. Firstly, the log-polar coordinate transformation method is used to convert the angular displacement measurement of the speckle image in the cartesian coordinate system to the displacement measurement under the log-polar coordinates. Secondly, the angular displacement measurement of speckle image is realized by using speckle correlation method and nine-point quadratic surface fitting method. Finally, the effectiveness of the method is verified by simulation experiment and physical experiment. The experimental results show that the mean error of the angular displacement measurement is controlled within 0.06° and the standard deviation is within 0.02° with the angular displacement range of [0°, 90°]. This method effectively improves the range and accuracy of the angle displacement measurement of existing speckle correlation method.