Yes, you can sign your commits! GIT supports it out of the box.
Sample signed commit git.blindage.org/commit/e1a24a6814082efb74cbad924c68a40b505f4e74
At first, create your secret and public keys, I wrote earlier about it (for english speaking users).
Check your keys
Add your fingerprint to your git configuration
$ git config --global user.signingkey A37721C3
Now you can sign your commits!
$ git commit -a -S -m 'fixed bugs, added new'
Here you can read full git documentation about this great feature. Auto-signing of all your commits https://gist.github.com/mort3za/ad545d47dd2b54970c102fe39912f305.