The correlation alignment algorithm (CORAL), a representative domain adaptation algorithm, decorrelates and aligns a labeled source domain dataset to an unlabeled target domain dataset to minimize the domain shift such that a classifier can be applied to predict the target domain labels. In this paper, we implement the CORAL on quantum devices by two different methods. One method utilizes quantum basic linear algebra subroutines to implement the CORAL with exponential speedup in the number and dimension of the given data samples. The other method is achieved through a variational hybrid quantum-classical procedure. In addition, the numerical experiments of the CORAL with three different types of data sets, namely, the synthetic data, the synthetic-Iris data, and the handwritten digit data, are presented to evaluate the performance of our paper. The simulation results prove that the variational quantum correlation alignment algorithm can achieve competitive performance compared with the classical CORAL.