Are there any misuse-resistant asymmetric encryption schemes?
Both require random elements for security, and it seems to me that both would not achieve semantic security (IND-CPA) if these repeat as RSA is otherwise deterministic.


Actually, that would be true of any potentially misuse resistant system.  As long as you don't fold in fresh randomness, and as long as you don't update long term state during the encryption, then encrypting the same message a second time will result in the same ciphertext.

Doing an SIV-like trick wouldn't help; if you encrypt the same message with the same private key, the PRF would generate the same nonce, and everything becomes deterministic.

What the PRF would help you if there are weak nonces (for example, in ECDSA, if you use the same nonce twice for two different messages, you leak the private key).  If there was a similar weakness in the public key encryption scheme, that would help.

On the other hand, I don't believe RSA-OAEP has such a weakness; hence the PRF idea doesn't make anything better