If you have a PGP key, you can sign in by signing a short challenge with it. Put your public key on your website, and link to it from your home page with rel="pgpkey":
<link rel="pgpkey" href="/key.asc">
The file is your public key in its ASCII-armored form, the text that starts with -----BEGIN PGP PUBLIC KEY BLOCK-----. With GnuPG, you can make it with:
gpg --armor --export you@example.com > key.asc
When you sign in, you'll be shown a challenge to sign. Sign it with your key, for example by pasting it into gpg --clearsign, and paste the signed message back in. Any OpenPGP tool that makes a clear-signed or armored signed message works.
RSA, DSA, ECDSA and Ed25519 keys work, including keys that sign with a separate signing subkey. A key that has been revoked is refused.