The cost of a car in 1920 varied wildly depending on the make, model, and features. There wasn't a single "average" price. However, a reasonable range would be from $500 to $3000.
A basic, smaller car could be purchased for closer to the lower end of that range, while a more luxurious or larger vehicle would cost significantly more. Keep in mind that $3000 in 1920 has considerably more purchasing power than $3000 today.