The antenna has to be resonant, so adding a random length of wire would probably decrease reception. (There are many more lengths that are not resonant than lengths that are - at any given frequency.) The antenna is probably the same design as all other cellphones use, and the problem could be either a receiver with low sensitivity or a transmitter with low power. (If the router can't hear the phone, you get the same problem that you get if the phone can't hear the router.)
Also, make sure that there are no other 2.4GHz devices operating in the area (like microwave ovens or older cordless phones), that there's nothing large and metallic (large being even as large as a saucer) between the phone and the router, or very near either one, and that the phone and the router are not too far apart vertically. (The antennas on routers are aimed around the router. The worst point is directly above or below the router, but being a floor or two above or below the router gives you very poor range.) Metallic wiring in the walls and metal wall studs also cause problems.