I think there's a bit of yes and no in this.
One of the things that got loads of people excited about Facebook shares was the 2012 Searchmetrics ranking factors report - here are the US and UK reports.
You'll see there that the report puts FB shares at the top of its correlation table - as if to say that pages with more shares ranked higher in Google.
The problem is correlation does not equal causation.
What I've found is that social signals can give your page a good short-term boost for a ranking term. If you're aware of the freshness part of the algorithm that gives a short-term boost to new pages in the search engine results, if those pages also have social signals to back them up, I think you're very likely to see a short-term benefit.
In the long-term, however, there is no substitute for links. In my own tests that have tried to measure the effect of (real) facebook shares on a page vs links, those with good links sustained the rankings. To me this makes sense if you think about it - Facebook shares and other social signals are much more easily manipulated.
What is clear though is that social signals are important - getting a lot of them can help your page to rank in the short-term and if you combine that with authoritative and legitimate links, you're definitely on to a winner.
Always aim to accrue Facebook likes and shares but don't see them as a ranking factor (or just a ranking factor). Someone sharing your page is a pretty strong endorsement for that page's content - if you can increase your shares for your page then you can be sure that your content is on the right track.
Hope this helps.