Jailbreak iOS 7 on iPhone 4 is entirely possible since the very first day of iOS 7 Beta 1 release, but majority of jailbreak developers tried to fabricate the fact and hide it from general users. In one way they have done an awesome job by avoiding releasing the developers-only jailbreak in public and the other way they neglected their purpose of bringing restriction free knowledge to users.
One can Jailbreak iOS 7 on iPhone 4, because it is the only A4 device currently in the market that has received an iOS 7 update from Apple. If you remember correctly then you must agree with me here that A4 devices are all vulnerable to GeoHotz Limera1n exploit that has actually allowed other hackers to easily sneak peak in next-generation iPhone operating systems for Untethered Jailbreak iOS 7.
In the past, we are used to receive updates of tethered jailbreak from iPhone DevTeam. The guys behind Redsn0w has stopped updating their tool, and decided to take a part in Evad3rs team. They refused to launch the Redsn0w with iOS 7 Jailbreak in public to avoid other hackers from receiving overwhelmed response from general users.
However, if Redsn0w is not updated with jailbreak iOS 7 support than here we have got some other open-source tools to jailbreak iOS 7 on iPhone 4. Yes, the guide itself is not for general users but with some basic knowledge of Linux and iPhone system you can perform the jailbreak iOS 7.
How To Jailbreak iOS 7 on iPhone 4:
Users can download Opensn0w from github, and compile it to use for jailbreaking iOS 7 on iPhone 4. The Opensn0w is an open-source program for iOS 7 Jailbreak by Winocm. While Winocm has revealed that he is not interested in bringing Jailbreak iOS 7 for public, he made his research & tools publicly available to all developers around the world.
Jailbreak iOS 7 on iPhone 4 (GUIDE):
Here I have found an interesting guide to jailbreak iOS 7 on iPhone 4 with OpenSn0w. You can follow the guide to jailbreak iOS 7 on your iPhone.