If you're using Slick2D to create the rectangle. Slick2D has a Shape class that can be used to describe such things (rectangles, circles, etc.).
I imagine you're using a shape like this for collision because it has methods like intersect()(link) that allow you to detect such things.
Shape also has a nice method called transform()(link). It can be used to apply a transform to your shape. Transforms are essentially matrix operations. Luckily you don't need to know too much about the matrix operation because it's easy to create transforms. Transform has a static method called createRotateTransform. You can use this to specify a rotation to create a transform to apply to the shape.
So the short of it would be, use something like this:
rotatedCarShape = carShape.transform(Transform.createRotateTransform(radiansToRotate)));
Remember that transform does not alter the original shape, so you don't have to worry about the rotations adding up, but you do need to remember to draw the correct transformed shape.