Can my 3.2V LiFePo4 battery power my cell phone through the cell phone's micro USB port?
The USB port on the phone expects 5 volts in. I doubt the phone will do anything if you give it less than 4.5 volts or so, though it might be possible.

But if you were to use a boost regulator to generate 5 volts from the external battery, at least that would work for powering the phone. Connecting to the +5V and ground lines of the USB connection should be enough, but phone chargers also connect some resistance to the data lines (or connect them together) to indicate that they're a charger instead of a real USB host.