Like the CaptainSauce said. Twitter is a network too. That being said, networking is a great way to promote you channel. It's an important part of developing and audience into a community that interacts with you, each other and your content. I love twitter. I get to talk to my subscribers and other creators. Just today, actually, I tweeted to the biggest youtuber of a certain game I love to play (see image). He responded and thousands of people saw our interaction and as a result looked at my profile. Perhaps analytics will later reveal that some of those people came to my youtube channel.
Additionally, when you share your content on twitter, you are increasing the SEO value of your videos. Without being overly complicated, suffice it to say that google promotes videos with more external links to them more than stagnate, not shared content.
Finally, don't just make a twitter account and spam your content. Instead, find other people who are talking about the same topics as you and interact with them. If you're a gaming channel, search the #(insertyourgamehere) and see who's talking about it. Talk to those people about the game, develop a legitimate relationship, and later on they will be fans of your content rather than one time viewers.
Hope this helps, and good luck!