To help your account be seen as an authority, you need to make sure that you:-
Offer quality, not quantity when it comes to Tweets
With only a small number of characters available to you per tweet, it’s important to think about what you want to get across, and to include all the information necessary. Again, short and sharp pieces of information that remain in your follower’s mind are recommended. Your tweets should keep your followers curious and leave them wanting more.
Keep your Twitter account updated frequently
People like to see something new. If there hasn’t been a tweet for a month, then your followers and profile visitors could just assume that you are not active anymore and they will stop following or visiting your Twitter account. To overcome this and keep visitors coming back, make sure you have an interesting profile page that is constantly updated, as visitors will want to find out what will be on your profile next.
Re-tweet someone else’s tweet
By interacting with others in the Twitter-verse, you will not only be able to build brand awareness but also a loyal following that will stand by you. It will change how you are perceived online and your followers will also be able to trust you more. If people start recognizing that you and your website provide excellent content, they would sub-consciously not hesitate to re-tweet your stuff. Once, they start doing that, becoming an authority will not take much time.
Ultimately, Twitter is beneficial not because of the SEO advantages it provides but because it helps in building relations with people and increasing brand awareness. In the long run, both these things combined will help your website more than higher search engine rankings.