The most straightforward answer to your question is a big, fat NO!
Social signals do not by themselves impact your rankings.
With that said, if your brand gets mentioned a lot on Twitter or your content gets retweeted a lot, you can benefit in terms of search engine rankings when bloggers or influencers on Twitter build links to your site.
For example, people following your niche keep seeing your content or your brand, they might want to check out your blog.
If they like what they see, they might blog about you or criticize whatever it is you've posted.
This counts as a backlink.
There has to be a link from somewhere outside of Twitter for you to get some sort of SEO mileage from your site's mention on Twitter.
Again, to recap, just having your link appear on Twitter is not going to help you.