Not now, but it might happen in the past. In 1999, Mars Global Surveyor discovered some magnetic
stripes on southern highland of Mars. The stripes resembles to the those found in Atlantic sea floor. On Earth, such
stripes are formed by a tectonic process called sea-floor spreading. Magma rose from the mantle forms new crust and slowly squeezes old one aside. Since the Earth's magnetic field alternates from north to south about every 10,000 years, the iron-bearing minerals in the crust magnetize and "memorize" the direction of the prevailing magnetic field, just like a magnetic tape recording the geological evidence of aeon.
The stripes on Mars are not only wider than those on Earth, but they are also stronger magnetized. This may mean that the Martian crust could have been generated at a greater rate, or the magnetic field of Mars, generated by its iron richer core, alternated less frequent than that of Earth.
Nonetheless, the Martian curst had stopped moving for the past billions of years. Smaller than Earth, Mars lost its heat much quicker and the once molten crust had fused together. With the same reason, the core became too viscous to generate a magnetic field.
If the magnetic stripes on mars are confirmed to be caused by plate tectonics, this would be the first direct evidence of the existence on another world other than Earth of such geological process.