You have not indicated what specific microcontroller you are utilizing.
However, you might consider a ESP8266 based module, which are quite inexpensive and can be programmed using the Arduino IDE with the proper compiler version.
They also offer a firmware which provides AT commands and LUA firmware as well.
They are available in several versions ranging for the simple module below for $2 to $3 on eBay:
WiFi Module - ESP8266
To a more feature rich version with USB programming support and full pin breakout like the NodeMCU in the $10 range:
**broken link removed**
There are other possibilities, Lantronix, Moxa, WizNET, etc., all of which offer WiFi compatible Ethernet controllers.
The prudent choice depends largely on the desired features, price and your comfort level and programming abilities.
BigDog