Using Tesla's Model 3 electric car and American driving patterns as an example, it is entirely possible that electricity needs for every driver could be met with renewable energy.
In short, if every driver in the world was a typical American driver then we would need to double the amount of energy from renewable sources in order to meet this new demand without affecting any other energy consumer. This would be quite expensive currently, however it is far from impossible.
Tesla's Model 3 standard and long range versions have battery capacities of 50kWh/75kWh, respectively, and ranges of 220miles/310miles. This gives us about 4 miles per kilowatt-hour of electricity for that electric car, and for simplicity let's just assume that's a good average.
The US Department of Transportation claims that the average American driver drives about 13,500 miles per year, and that there are 210 million Americans with a driver's licences. Assuming they all count as 'drivers' for the first statistic, that's roughly 3 trillion miles driven by Americans per year. So, assuming 4 miles/kWh and 3 trillion miles, America would need to produce roughly 750 billion kWh of electricity per year to power electric cars for all current drivers.
A quick look at a list of countries by power consumption on Wikipedia shows that the US consumes about 3.9 trillion kWh per year. Assuming the 750 billion kWh estimate is good enough, about 20% of America's current total energy consumption would have to go towards electric cars. According to REN21's 2017 report on renewable energy, renewable energy accounted for 19.3% of global energy consumption.
So, if America increased it's energy production by 20% and only through renewable energy sources, then the electricity consumption by electric cars would be met without affecting any other consumer. Although expensive, this is certainly in the realm of possibility, and the actual worldwide increase would probably lower due to smaller percentages of drivers outside the US.
Trucking addendum: In case the above DOT stats on miles per year only apply to 'typical' drivers and not truckers, here's some trucking info:
The American Trucking Association claims that about 450 billion miles were traveled by trucks in 2015. Assuming electric trucks are a quarter as efficient as electric cars, it gets 1 mile per kWh, for an additional 450 billion kWh on top of the 750 billion kWh above for a total of 1.2 trillion kWh. This means that even if trucks weren't counted in the previous DOT statistics then the increase would be about 30% rather than 20%. Even more expensive, but still possible.