There is no jailbreak available for your device running iOS 6.1.3. However, you could choose to downgrade your iOS to 6.1.2. I can't provide a link to iOS 6.1.2 due to legal issues, however, a google search should bring it up.
Once you have the file, open iTunes on the computer. Go to your iPhone 4S page, and hold shift while pressing restore. Choose the iOS 6.1.2 file, and wait for a while. This will make your iPhone 4S run iOS 6.1.2.
From there you can jailbreak your iPhone 4S by going to: http://evasi0n.com/ and downloading the "jailbreak-er" for windows, mac, or linux. Follow the onscreen instructions to jailbreak your iPhone 4S and you should be all set!!!