Partial point cloud registration is a challenging problem, especially when the robot undergoes a large transformation, causing a significant initial pose error and a low overlap. This work proposes exploiting equivariant learning from 3D point clouds to improve registration robustness. We propose SE3ET, an SE(3)-equivariant registration framework that employs equivariant point convolution and equivariant transformer design to learn expressive and robust geometric features. We tested the proposed registration method on indoor and outdoor benchmarks where the point clouds are under arbitrary transformations and low overlapping ratios. We also provide generalization tests and run-time performance.