Official site for Evasion jailbreak ios 6.1.3 by Evad3rs Team: http://www.evad3rsteam.com/

iOS Jailbreak 6.1.3 has been released. We liberate yours iPhone 4S and iPhone 5. You can download Jailbreak 6.1.3 with just one click and save it to your PC or Mac. It's new tool for iOS 6.1.3 iPhone 4S, iPhone 5, iPod Touch 5G, iPod Touch 4G and all iPads with iOS 6.1.3. Untethered 6.1.3 Jailbreak has been released. Freedom for all idevices. Cool. Yeahhh.

How to jailbreak iOS 6.1.3 Tutorial:
Download the evasi0n tool for ios 6.1.3 jailbreak untethered.
Open the evasi0n jailbreak 6.1.3 tool
First connect your iDevice to your pc/laptop windows, Linux or mac.
Make sure your iTunes is closed before proceeding.
Hit the jailbreak button and wait a few minutes.
After iDevices is turned up you can check cydia is working and also restart your iDevice to check the 6.1.3 jailbreak is really untethered