Yes, Twitter can be useful for increasing traffic for website and enhancing backlinks by actively participating during conversation with relevant users.
Twitter is without any doubt a good way to find and engage more people that would make traffic on your website. But you need to work every day on that.
Following ways to Twitter can be useful for your business are:
Communicating
Generating leads
Showing your brand's personality
Researching trends
Providing customer service
Yes, Twitter also useful for your business. In early stage in twitter do hardwork for your website after that you can increase website traffic and brand awareness.