There are at least three sites online that cover this:

 - [Jaunted][1]
 - [Wi-fi Free Spot][2]
 - [Airport Hotspot Finder][3]

When I asked a [similar question about Astana airport][4], my eventual solution was to use [Foursquare][5] - if people have checked in there, there's a good chance they had wifi, or may even mention it.  I found the [relevant page][6] for the airport and voila - lots of mention of the wifi.

Also I nearly marked this as a dupe, but you may want to check out other free wifi links in a [similar question on whether there are listed free wifi hospots around the world][7].


  [1]: http://www.jaunted.com/maps/Airport-WiFi-Map
  [2]: http://www.wififreespot.com/airport.html
  [3]: http://usatoday.jiwire.com/hotspots-hot-spot-airport-directory-browse-by-country.htm
  [4]: http://travel.stackexchange.com/questions/1304/is-there-wifi-in-astana-airport-kazakhstan
  [5]: https://foursquare.com/
  [6]: https://foursquare.com/v/astana-international-airport-tse/4bc3ef0a2a89ef3ba2c7f588
  [7]: http://travel.stackexchange.com/questions/1407/is-there-a-resource-to-find-free-open-wifi-hotspots