Here’s a link to a two-minute video in which Carri Bugbee explains how you can use Twitter to promote your fiction by having your character do the tweeting.
As she points out, you will still need to use other means to make people aware of the character.
When it’s a lead in a popular TV show that’s a lot easier than if it’s the protagonist of an unpublished novel or unproduced screenplay, but if the character is interesting enough and you have other ways of drawing people’s attention to what you’re doing, it might be a good strategy.
Look at it this way: if you try it and it fails because nobody pays attention to it, who will know?
By the way, I do post occasionally on Twitter; if you want to find me on there, my user name is jurgenwolff (and I promise I won’t inundate you with reports on what I’ve had for breakfast).