An elliptic curve key is probably memorizable (a 256-bit number essentially) but is not quantum-resistant. For quantum-resistant schemes you might be able to memorize a 256-bit seed for a key generation algorithm. You can look at bitcoin "brain wallets" as precedent - they basically translate these random seeds into a memorizable phrase.

That being said, people are unlikely to bother memorizing a 256-bit key, and even if they do they'll just type it into a shady form in a phishing email anyway. Better to just put it on a smartcard chip - it's proven technology that's been rolled out in other nations already.