When Google Inc. launched its Google+ social-networking site three weeks ago, executives handed out sailor hats to the hundreds of employees working on the project, symbolizing their year-long journey to that point.

So far, the sailing has been mostly smooth. On Wednesday, Web-traffic watcher comScore Inc. estimated Google+ has had 20 million unique visitors since its launch, including five million visitors from the U.S. A Google spokeswoman declined comment.

ComScore,...