Do you think cellphone towers are affecting the birds population?

I would say wind turbines and solar farms are far more a threat to the bird population than cell towers. The reflective surface of solar panels can reflect and concentrate the sun's energy to strike birds in mid-flight and wind turbines can slice and dice birds. You know, when wind turbines are actually getting wind to operate. In the California desert they tend to be more for decoration.

The standard practice of radio engineering is to only use the amount of power necessary to send communications. Cell towers generally put out less energy than television and radio station towers. Also, even though the frequencies are within the microwave band the electromagnetic radiation from cell towers is non-ionizing so it can't cause damage to DNA. The worst the EM from a cell tower can do is vibrate the water molecules in cells which can cause RF burning if you actually touched the antenna while it is transmitting.

The amount of cell tower radiation people normally get at ground level is negligible. Birds may get slightly more exposure because the tower's energy is directed parallel to the ground. Even then due to the inverse-square law that extra exposure is still negligible.