Are you using the twitter account for business or just personal use? I've seen business run contests etc. on their twitter feeds to gain a huge following.
I've found the easiest way as addmefast or youlikehits add your site on these social network tools and earn points for spending them for your posts and you'll get followers for your sites very easily.
Its so difficult to find a tool that increases twitter followers, as there are many scammers they use these tools to get your account's password. I'd suggest you to try buying twitter followers, you can try SEOclerks, there are many freelancers on this website providing twitter followers at a cheap rate.
I would recommend you to do the organic way such as regularly update/tweet and adding hashtags to engage some conversations and then with this you would get some followers and also share your Twitter profile on social media websites such as your personal facebook profile and your fan page if you have one, and share it in some groups if you have any on Facebook. Share it on Google+ as well and leave a wall post on Facebook asking your friends if they have Twitter to follow you and do the same with other social media that you have account on. This would make your twitter profile to look better because if you get so many followers with so little tweets then people would think something is up. I cannot stand any Twitter profiles has so many followers without doing anything to earn these followers. That is my own opinion though, some of other people may have different opinion than mine. Not only sharing your Twitter profile on social media, share it in your signature and your profile on some community and use your Twitter profile as a signature such as E-mail and if you are writing a comment somewhere or such like this example: That's just a example of what you can do as your signature when writing a comment or responding to something like on Yahoo Answer, Email and others.
Use social exchange websites. Like addmefast. And if you need actual followers you need to do social media marketing properly.
Using tools will not make any sense when you want real followers, manual followup from niche related people will give you better exposure. your tweets should be interesting and if possible add some contributing links where from people can get required information. there are few follow-back groups around twitter where from you can easily find people with genuine account, you should start searching for popular people in your industry and there will be loads of followers you will get by joining the conversion and it works well as you get rid of fake followers.