You can. I’m not particularly familar with Thunderbird, but you can export your key to system/user keyring then you can sign any data you want using GPG. However, I doubt tool exists for you to embed the signature to a PDF like x.509 signing would.

https://superuser.com/questions/653231/embed-a-gpg-signature-in-a-pdf-file#1361205

Do you mean using PDF’s built-in signature mechanisms? I don’t think so.

If you want to do regular PGP file signing you can export the key from Thunderbird and do whatever you want with it.

Thank you all for your quick reactions !!

To summarize if I want to use the PDF built-in signing I will need to convert my OpenPGP into a X.509 cert otherwise I can simply use the OpenPGP file signing

I want to stick to the UNIX Philosophy especially:

Write programs that do one thing and do it well.

So I will use the OpenPGP signing tool :)

Thanks !