Avira does have some rootkit detection ability. I'm not sure if it scans automatically but you can use the manual "rootkit search" scanner.
You can also try Gmer which is good. I believe Rootkit Revealer is also good and in the past I have used IceSword.
It's important to follow the instructions because they are powerful tools. You may also need to read about what the results mean and/or post the results on a forum dedicated to the program and/or rootkits.
Edit: Be sure that your version of Windows supports the detector that you try.