Is there a jailbreak for Iphone 4 with a 6.1.3 iOS?

Just would like to know if there was a way to jailbreak my Iphone 4 with the 6.1.3 iOS?

Yea Download evasi0n

You can't use evasi0n to jailbreak your iPhone 4 on 6.1.3. You will need to use Redsn0w.

Keep in mind that it will be tethered. If you know what it means, you'll understand how majorly inconvenient that is. But I'd rather have a tethered than non-jailbroken.

There isn't an untethered jailbreak for ios 6.1.3.
For the ipod touch 4g, iphone 4, there's a tethered jailbreak, which requires you to have your computer to turn it on whenever it gets powered off.