iOS 6 beta 1 has been jailbroken but unfortunately Cydia is not compatible with the latest firmware and is broken.However, iDB has come up with a tutorial on installing Cydia on iOS 6 beta.
How to install Cydia on iOS 6 Beta
1. At first you need a jailbroken device with RedSn0w 0.9.13dev1 running iOS 6 Beta firmware.
2. SSH to your device, for Windows you can use Putty and Mac users can use Coda.SSH username = “root” SSH password = “alpine”.
3. Execute the following command via SSH:
wget -q -O /tmp/cyinstall.sh http://wyndrepo.googlecode.com/files/cyinstall.sh && chmod 755 /tmp/cyinstall.sh && /tmp/cyinstall.sh
4. After the SHSH command your device will respring and Cydia will appear on the Home Screen.
5. Tap to open Cydia and then it will prepare its filesystem.Cydia will respring again and then you can start using it.
Note: There might be bugs in iOS 6 beta so install Cydia at your own risk.