I have been on Twitter for over a year now, and have built a pretty decent following by spending a substantial amount of time tweeting with others. You get 140 characters to create a post, which has helped me with the elevator pitch in real life. Just talk to somebody like your tweeting and they will be able to get a word in!
Twitter has come a long way during that time, including adding 3rd party programs like Sponsored Tweets, so you are able to profit while working your social marketing.
If you have a loyal group of followers, even if it is a small group, you now have the opportunity to tweet out specific messages containing an advertisement that you approve.
In addition to having the opportunity to do sponsored tweets, you also are able to participate in affiliate programs and make a commission from other tweeters who send out sponsored tweets.
Don't worry about your followers getting turned off by the sponsored tweet messages. Just make sure that you are putting quality tweets out in between the sponsored tweets messages and you will do fine.
You can also use programs like Ad.Ly and MyLikes to send out sponsored tweets.
It doesn't matter if it is your website, your blog, Facebook or Twitter; it all comes down to the personal relationship and the quality of your content. If it's good, you will have people engage, if you constantly spam, you will lose your reader.
Let me know what program you choose to use, maybe you will sign up for both?