Do you mean installing the drivers? According to the official page, this should not be needed. I tried installing them anyway, but it didn’t solve the problem:
As you’ve already noticed, unfortunately the chip set manufacturer ASIX hasn’t provide the device driver of the USB 2.0 Gigabit Ethernet adapter (chip set AX88178) yet. As far as we have tested in-house, the adapter won’t work after upgrading into 10.12.
We’ve also tested our USB3-E1000 USB 3.0 Gigabit Ethernet adapter (chip set AX88179) and USB2-E100 Fast Ethernet adapter (AX88772) with 10.12 and the latest device driver, then verified they worked fine.
We’ll contact ASIX to see if they could provide the Estimate Time Arrival of the newer driver for Mac OSX 10.12. If we could get the answer, we’ll update it in here.