You generally don't need to report winning a car to the IRS *unless* its value exceeds $600. If the value is over $600, it's considered a prize and you'll need to report it as income on your tax return. The fair market value of the car at the time you won it is the amount you report. You'll likely receive a Form W-2G from the organization giving you the car if it's a substantial prize.
Therefore, the answer depends on the value of the car. A car worth less than $600 doesn't need to be reported, but one worth more than $600 does.