There are different possibilities to create a log signature and append it automatically to your logs.
The best solution for you depends on the way you like to log your found geocaches.
As others have mentioned there are c:geo (Android App) and GSAK (PC program to log from field notes) that support signatures.
If you prefer logging geocaches by the geocaching.com website I would recommend to look at the user script GC Little Helper:
It comes with a lot of nice features including log signatures.