I didn't use this network adapter myself yet, but according to lots of other discussions it is (or at least was) working with ESXi. What you may do is to ensure the NIC is properly detected by the host's BIOS, and you may also try to boot from e.g. a Linux Live CD to see whether this detects the NIC. If this is the case and the NIC still doesn't get detected by the latest ESXi 5.5 build, try to use an older build to see whether this works.
André
PS: I just checked the Intel drivers which are included in the different v5.5 builds, and it looks like the "net-igb" driver was replaced with Update 1. So I'd suggest you try to install the ESXi 5.5 GA release, which includes the older drivers.