Folks at AppAdvice have figured out a way to get root access to an iPhone 4 running iOS 7 beta 1 without jailbreaking the device.

The procedure is fairly long involving quite a few steps and tools. For a detailed guide, click on the source link below or watch the video embedded below:
They seem to be using an external ramdisk exploit for iPhone 4 to gain access to the file system. This isn’t anywhere close to a jailbreak, since that would require patching the kernel to get around code signing and other restrictions, which means there’s no Cydia and the ability to install jailbreak tweaks.
You still can do some pretty cool things with just read write access to the entire filesystem, like modifying plist files, changing app icons, as shown in the video and so on.

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