No, usually you are required to use hybrid cryptography.
ECB, CBC etc. are defined for block ciphers. Although you could possibly apply them to asymmetric cryptosystems, it would make little sense:
- performing sequential asymmetric cryptography is not efficient, block ciphers are much more efficient
- in general there will be a lot of overhead per block, e.g. due to per-block padding (where block ciphers don't have any overhead per block)
- the block size is usually rather large
So in general a symmetric key is generated, which encrypts the plaintext, and then the symmetric (session or data) key is encrypted and send with the ciphertext.
Note that ECB is usually not secure. For asymmetric ciphers, the plaintext (or key) is normally wrapped with random padding before encryption. So ECB is not deterministic for most asymmetric encryption primitives for which such random padding is applied.