In this paper, a geometrically invariant color image watermarking method using Quaternion Legendre-Fourier moments (QLFMs) is presented. A highly accurate, fast and numerically stable method is proposed to compute the QLFMs in polar coordinates. The proposed watermarking method consists of three main steps. First, the Arnold scrambling algorithm is applied to a binary watermark image. Second, the QLFMs of the original host color image are computed. Third, the binary digital watermark is embedding by performing the quantization of selected QLFMs. Two different groups of attacks are considered. The first group includes geometric attacks such as rotation, scaling and translation while the second group includes the common signal processing attacks such as image compression and noise. Experiments are performed where the performance of proposed method is compared with the existing moment-based watermarking methods. The proposed method is superior over all existing quaternion moment-based watermarking in terms of visual imperceptibility capability and robustness to different attacks.