In this paper, a weighted similarity-invariant linear algorithm for camera calibration with rotating 1-D objects is proposed. First, we propose a new estimation method for computing the relative depth of the free endpoint on the 1-D object and prove its robustness against noise compared with those used in previous literature. The introduced estimator is invariant to image similarity transforms, resulting in a similarity-invariant linear calibration algorithm which is slightly more accurate than the well-known normalized linear algorithm. Then, we use the reciprocals of the standard deviations of the estimated relative depths from different images as the weights on the constraint equations of the similarity-invariant linear calibration algorithm, and propose a weighted similarity-invariant linear calibration algorithm with higher accuracy. Experimental results on synthetic data as well as on real image data show the effectiveness of our proposed algorithm.