You must use a WiFi (2.4 GHz) antenna. From the picture in your post, you have one of the esp8266 modules with a "built-in" antenna implemented via traces on the PCB. You cannot add an external antenna without removing the old one first, and even that will be very dodgy - you'll likely render your esp8266 useless for any purpose.
Instead, you could get an esp8266 that is made for connecting an external WiFi antenna. See the Wikipedia article for details. It specifically mentions model # ESP-WROOM-02U as having a connector for an external antenna.