Can you jailbreak ios 6.1.3?

Yes, there is a snowbreeze jailbreak for 6.1.3 and a work around for redsnow if you have shsh blobs. but they are tethered jailbreaks. They are videos on how to make them into semi-untethered, but waiting until a evasi0n untethered release for 7.0 would be possibly a better idea. Also stay away from fakes like silver wind for example. Tethered means you need a computer to turn your device on if it dies and run the software again. Semi-untethered means you can turn it on, but need to run software to get full acess to jailbreak, safari, etc. Hope this helps and yes it is only on a4 devices.