Theoretically, couldn't he just have his engineers tweak the Facebook algorithm to make him President? Figure out how many swing state voters you need, set their Facebook feeds to deliver positive news about Zuckerberg and negative news about rivals.
I doubt it would even be ruled illegal in the current landscape. I'm sure the media would raise a stink, but the voters you care about would never see those scathing op-eds.
I personally think Bill Gates should run, he'd be a much better President, and much more likely to win.