Daniel Becker, Patent Attorney and Early-stage Engineering (2013-present)
Sure, it is possible to make a 100% renewable energy car. However, it does depend upon how many asterisks you can tolerate on that answer.
Almost all of the solutions require presuming that you will consume the energy in an electric vehicle. If you have a solar charging grid, then that can be used to store energy in a battery, like Tesla’s powerwall, or any other number of custom solutions, and then it can be used to charge an electric vehicle.
In the future, or in probably some places in the world with lots of geothermal or wind energy, then solar may not be the only option. Also, hydroelectric is without consumption of fuels, but that isn’t as easily able to be proliferated around the world, because there are relatively few places with large rivers to dam-up. By comparison, the sun is available in useful quantity most places on the globe.
However, I am presuming that your question only means that the vehicle is powered without fossil fuels. Do you mean for the ENTIRE car to be produced and run through its entire life cycle without the consumption of non-renewable energy?
Now THAT could be very difficult. Electric cars require mining for lithium, for one thing, and batteries do wear out. And transportation of all of that massive amount of chemicals requires industrial and commercial transporation and freight, and that seems very unlikely to become focused upon renewable energy in the near future.
Manufacturing just takes too much energy, and it requires a steady supply of affordable and instantly variable amounts of it. Gas turbine generation, nuclear, compressed natural gas, fossil fuel energy generation are ubiquitous, well-practiced, mature technologies that are far cheaper than providing custom solutions of newer and rapidly-developing technologies.
I think that you meant the first part, though; a car that is entirely fueled with renewable energy.