With the increasing demand for geographic information and position information, the geographic information system (GIS) has come to be widely used in city planning, utilities management, natural resource environments, land surveying, etc. While most GIS maps use vector data to represent geographic information more easily and in greater detail, a GIS vector map can be easily copied, edited, and illegally distributed, like most digital data. This paper presents an invisible, blind, secure, and robust watermarking method that provides copyright protection of GIS vector digital maps by means of arc length distribution. In our method, we calculate the arc lengths of all the polylines/polygons in a map and cluster these arc lengths into a number of groups. We then embed a watermark bit by changing the arc length distribution of a suitable group. For greater security and robustness, we use a pseudo-random number sequence for processing the watermark and embed the watermark multiple times in all maps. Experimental results verify that our method has good invisibility, security, and robustness against various geometric attacks and that the original map is not needed in the watermark extraction process.