Make sure that your website twitter sharing buttons mention "via @YourTwitterAccount" this does help you get more followers. Use 2 or 3 max hashtags in your posts so that when people search for your keyword they find your tweet.
Add your twitter account in forums and when you do guest blogging. Use the search feature to find any questions related to your website/niche then answer those questions then the person might check out your profile and follow you. Don't reply with a link, reply with a solution.
Include a link to your twitter profile at the end of each email you send. Also use something like "retweet for a follow" in your tweets and when people retweet your stuff it will reach a lot of people and some of them will follow you.
Share blog posts from other popular bloggers in your niche and mention "via @TwitterAccount" when people see the popular name or brand they'll most likely retweet it which may get you more followers.
Keep your tweets short, this will leave space for tweeps (people on twitter) to add "RT @name" then your tweet. Don't be afraid of sharing your best content multiple times this will help you reach more people in different time zones, unlike facebook which uses an algorithm.
Ask questions, this will help you get more engagement and people will see your username shared by different tweeps and follow you.
Avoid flooding the feed, you'll get a lot of unfollows, have a space of more than 3 hours on your tweets. Use a twitter competition and offer a price to someone who'll get more retweets and favorites.
Design your profile and brand it properly, separate yourself from the average tweeps. etc. etc. etc.
Hope that helps