Random sample consensus (RANSAC) is a popular paradigm for parameter estimation with outlier detection, which plays an essential role in 3D robot vision, especially for LiDAR odometry. The success of RANSAC strongly depends on the probability of selecting a subset of pure inliers, which sets barriers to robust and fast parameter estimation. Although significant efforts have been made to improve RANSAC in various scenarios, its strong dependency on inlier selection is still a problem. In this paper, we propose to address such dependency in the context of LiDAR odometry by robust object-aware sample consensus (ROSAC). In the proposed ROSAC, the sampling strategy is adjusted to preserve object shapes and a new consensus method is developed based on robust low-dimensional subspace analysis. It is demonstrated in extensive experiments that the proposed paradigm works well in LiDAR odometry, achieving estimation of 3D pose with superior accuracy compared to RANSAC. Even for the case of RANSAC failure, ROSAC still achieves up to 67% of improvement in accuracy compared to baseline LiDAR odometry. Since a partially parallel implementation of ROSAC already leads to a significant speedup, we believe it can be extended to other problems of parameter estimation with both higher accuracy and efficiency.