Is there a jailbreak for Iphone 4 on ios 6.1.3?

If so please like it in the comments!

Yes there's: Redsn0w 0.9.15b3

What you'll need:

Redsn0w 0.9.15b3

iPhone 4

iOS 6.0 firmware (It must be 6.0 for your device)

PC (Mac) with internet

White USB cable

How to:

Plug your phone in

Close all applications that open (especially iTunes)

Open Redsn0w

Click "Extras", then click "Select IPSW", click on the 6.0 firmware you downloaded, make sure Redsn0w accepts it, go back.

Click "Jailbreak" - Follow the on-screen instructions

Note: The jailbreak is tethered meaning that every time you need to fully power off or reboot your device, you'll need to plug it back in and boot it up into a tethered state with Redsn0w

Links are in Source