Yes it does support elliptic curve cryptography. It needs to be running ASA 9.4(1) or later and configured properly.
It's confirmed in the release notes here:
http://www.cisco.com/c/en/us/td/docs/security/asa/asa94/release/notes/asarn94.html
A good explanation of getting it to work with AnyConnect can be found here:
https://ltlnetworker.wordpress.com/2016/12/18/elliptic-curve-asa/