Because they will impact so many areas, copyright issues will inevitably arise as 3D printing expands into the content industry. The problem is that protections based on conventional methods are not effective, because the 3D printing process disables those protections. In this paper, we propose a robust and blind watermarking scheme that is able to protect content not only when the 3D model is shared in the digital world, but also when the 3D digital content is converted to analog content by 3D printing. First, we base our proposed watermark on a component that is unchanging to the printing direction for robustness against the printing process. The printing artifacts, instead of being regarded as severe distortion, are treated as a template that provides orientation information to the watermark detector. To achieve this, we also propose a blind estimation algorithm for the printing direction that starts from an analysis of the layering artifact. Using the results from a proposed estimator, the watermark from the printed-and-scanned model is synchronized with the original orientation. With the results of our tests with various 3D mesh models and attacks, we experimentally verified that the proposed method does not lose embedded patterns during the 3D print-scan process, especially with low-cost printers. Moreover, our method provides a new solution for estimating the printing direction that will be useful in a variety of fields.