Extrinsic calibration between a camera and a vehicle is crucial in real-world applications. Conventional motion-based calibration methods often rely on assumptions such as driving on a flat surface or along parallel lines, which restrict their performance in off-road environments. In this paper, we propose a motion-based targetless camera-vehicle calibration method that works in off-road environments. Our method introduces two key features. The first is the Normal Vector Alignment (NVA) constraint which aligns the vehicle's crawler contact area with the ground to mitigate the negative effect of rough terrain. The second is the data segmentation which divides the motion data into multiple segments to reduce drift error in camera motion estimation. We build a construction site dataset using real construction machinery and evaluate our method. The results show that our method achieves robust and highly accurate calibration in construction sites.