Would Rousseau use the Internet? It would seem so. He was a frantic publisher of his ideas and had many problems with censorship in his day. Being able to publicize his ideas freely would be a great boon for him. Even more so would be easy access to information and to ideas of others.
Would he have a website? Probably. He might even open a blog page.
Would he join social networks? Certainly not. Rousseau was a very self-centered person cherishing his privacy. He would not expose himself to contacts with unknown outsiders. In his day he quarreled with nearly all his acquaintances and even close friends. He also suffered from persecution mania, especially as he grew older. While he often criticized the ideas of others, he did not respond positively to criticism of his own views.
Rousseau might not react very positively to mass movements launched over the Internet. His view of the intellectual capacities of ordinary people was rather dim. The cult he enjoyed during the early days of the French Revolution would already have shocked him.