No, you should not click on links sent by someone you don't know. This rule of thumb applies to your activities on Twitter as well as anywhere else on the Internet.
Social networking sites like Twitter may seem safe, but in fact it's exactly this kind of “safe” feeling that cybercriminals take advantage of. Your guard is down and that makes you an easy target.
Several new scams have been popping up on Twitter recently, many involving false links. Some of these links, when clicked, display a fake antivirus alert designed to trick you into paying for software you don't need. Others lead to websites that will install spyware on your computer.
So, this person on Twitter may really be a new friend, or she may not be who she says she is. Don’t take the chance.