Can AES-NI be used to accelerate asymmetric encryption? AES-NI optimized processors can be used to accelerate AES, which is a symmetric crypto. Can it also be used to accelerate asymmetric crypto?
These are the AES-NI instructions listed by wikipedia:


AESENC:   Perform one round of an AES encryption flow
AESENCLAST:   Perform the last round of an AES encryption flow
AESDEC:   Perform one round of an AES decryption flow
AESDECLAST:   Perform the last round of an AES decryption flow
AESKEYGENASSIST:  Assist in AES round key generation
AESIMC:   Assist in AES Inverse Mix Columns
PCLMULQDQ:    Carryless multiply (CLMUL)


If the asymmetric crypo in question were to use any of these operations, then yes, it could be accelerated by the appropriate hardware instruction. 

However, standard asymmetric primitives such as RSA and Diffie-Hellman do not use these sorts of operations. Without knowing specifically what asymmetric algorithm you had in mind, we can conclude the answer is probably "No".