According to the security firm, Kaspersky, this is the first attack to target Twitter. However:
two worms that target social networking sites MySpace and Facebook. More variants of these worms are also starting to turn up.Read more on BBC NEWS | Technology | Hi-tech criminals target Twitter
Always be suspicious of any site that wants you to download any file that ends in .exe, which means it is an executable file. Once you have downloaded the file and click on the .exe, you have given up control of your computer if the .exe file is a trojan. This is true of any email attachments as well as files you will find on the Internet.
Be safe out there.