Is fuel cell a renewable source of energy?

No, it is not a renewable source of energy.

Fuel cell is a means of storage energy, for example hydrogen can be produced from any primary energy source; renewable (as solar energy) or exhaustible (as coal or oil) and then stored as energy in the fuel cell. When energy is needed later on as electricity then we can get from the fuel cell. Fuel cells is very efficient as in intermediate energy storage system in a proposed global energy system that is completely clean energy system. In this system, hydrogen is produced (parallel with electricity) from renewable (like solar) or non-conventional (like nuclear) primary energy source.
Fuel cells have typically used hydrogen and oxygen as a power source. You can get these gases by splitting water (H2O) either by electrolysis or by what we call water thermochemical decomposition. In this thermochemical decomposition method water can be split into hydrogen and oxygen in some consecutive intermediate steps where special chemicals are used as catalysts to get this decomposition possible at practical temperature ranges.

As an aside: For the same amount of energy, coal produces more greenhouse gases (CO2) than gasoline. So, if your electricity is generated form coal (which is common), a fuel cell powered or electric car will probably produce more greenhouse gases than a gasoline powered car (of the same size, power, etc).
Electric powered cars are considered environmentally friendly so far as the electricity is produced from a renewable or non-conventional primary energy source.