Sony Ericsson Started Rolling out Android 2.3.3 Gingerbread official update few days ago,and right after official release the underground development community at XDA, has managed to attain root privileges.  Please follow the below listed instructions and root your device.

Instructions root stock Android 2.3.3 on Xperia X10 :

1. The first step is to download Flashtool package. Click here to download
2. The second step is to Enable Unknown Sources & USB debugging. Go to Menu -> Settings -> Applications -> Unknown Sources & Menu -> Settings -> Applications -> Development -> USB Debugging
3. Please turn your device off and open Flash Tool folder
4. In FlashTool select aZuZu_Kernel_DownGrade or use this one with FlashTool you already have
5. Please pay some attentions to instructions given on screen and Follow FlashTool instructions. When done, leave FlashTool running.
6. Now Remove usb cable and Power on device, after vibration connect usb cable immediately.
7. Wait till you see any info in FlashTool, then click root. After root is done. Phone will reboot.
8. If Phone didn’t reboot pull out battery 1-2 min and place it back.
9. In FlashTool select aZuZu_Kernel_UpGrade or use this one with FlashTool you already have >>> Kernel upgrade <<< .
10. Follow FlashTool instructions.
11. When done. Pull out usb cable.
12. Power on your phone and phone will be rooted.

Video Guide click here:

Incase if you are strucked somewhere and need further assistance you can contact the developer by visiting their official thread at XDA. Please do all the steps at your own risk.