Yes, but it takes a lot of wire! The magnetic field of the earth, at a given geographic location, doesn't change very much, and only changes in a magnetic field can be used to drive electrical currents in a wire. Typical changes in the Earth's field are measured in fractions of percent and are caused by solar and other geomagnetic disturbances out in space. 'magnetic storms' can cause up to a 1 percent change lasting several hours, and in northern countries these also coincide in the evenings with auroral displays. This means that any 'auroral electricity' you generate will be very unreliable and certainly not in constant supply, but come and go with the time of year, solar activity cycle, and other factors that make them unpredictable.
All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the
NASA IMAGE/POETRY project.