You can use your own unique logo for your Twitter public profile. This is useful if you want to create a brand for your website or blog. A logo can better reflect the nature of your site compared to standard photo image.
You cannot use an official Twitter logo to brand your profile or blog. The Twitter logo is trademarked and you can run into trouble if you use it without express permission from Twitter. It is best to create your own logo or use your existing one and post it on your Twitter profile.
There are several advantages of using a logo for your Twitter public profile. As mentioned earlier, a unique logo could help in creating a brand for your blog or website. Your network on Twitter will immediately recognize your sites once they see your logo. This is the best way to instill brand recall for your Twitter followers and to make your websites popular.
By using a logo for your Twitter account, you can highlight your creativity to your followers and network. With a standard photo, you cannot really design it or make artistic changes on it. But with a personal Twitter logo, the design possibilities would be unlimited.
This is important if you are a web designer or a graphic artist. By highlighting your logo on Twitter, people will be able to see your skills in designing graphic arts. That is why some Twitter users are using a personalized logo for their profile instead of the standard personal photo image.