In the last decade, Social Networks (SNs) have deeply changed many aspects of society, and one of the most widespread behaviours is the sharing of pictures. However, malicious users often exploit shared pictures to create fake profiles, leading to the growth of cybercrime. Thus, keeping in mind this scenario, authorship attribution and verification through image watermarking techniques are becoming more and more important. In this paper, we firstly investigate how thirteen of the most popular SNs treat uploaded pictures in order to identify a possible implementation of image watermarking techniques by respective SNs. Second, we test the robustness of several image watermarking algorithms on these thirteen SNs. Finally, we verify whether a method based on the Photo-Response Non-Uniformity (PRNU) technique, which is usually used in digital forensic or image forgery detection activities, can be successfully used as a watermarking approach for authorship attribution and verification of pictures on SNs. The proposed method is sufficiently robust, in spite of the fact that pictures are often downgraded during the process of uploading to the SNs. Moreover, in comparison to conventional watermarking methods the proposed method can successfully pass through different SNs, solving related problems such as profile linking and fake profile detection. The results of our analysis on a real dataset of 8400 pictures show that the proposed method is more effective than other watermarking techniques and can help to address serious questions about privacy and security on SNs. Moreover, the proposed method paves the way for the definition of multi-factor online authentication mechanisms based on robust digital features.