Smoothieboard v1 currently does not have a native Wifi interface.
However, it is possible to easily wake it Wifi-capable by connecting it's Ethernet interface to a simple Wifi/Ethernet bridge.
For example, this $15 Wifi/Ethernet bridge will easily make your Smoothieboard Wifi-compatible.
For instructions, see the manual of the bridge you select.
This also generally has the advantage of being much more reliable and efficient than an “on-board” Wifi system which can be found on a few other CNC controller boards.