@MatthewJensen has provided a very reasonable possible explanation. The OP has however indicated that the car left the parking spot before the rain. This prompts the consideration of an alternative mechanism:
A car has been parked there for some time in the hot sun. The surrounding asphalt in direct sunlight has heated up, while the asphalt beneath the car has remained relatively cool. The car has then left the parking spot, and there has subsequently been a small drizzle. This has evaporated quickly from the surrounding hot asphalt, but is in the process of evaporating more slowly from the cold asphalt where the car was located, and some water still remains there.
In fact, if we constrain ourselves to inside-the-box thinking in a car-in-the-rain situation and approach this as a physics problem, these two timelines (or some combination of them) seem to be the only ones possible:
Assume that the rectangular shape is due to a car, and that all the water has come from rain falling vertically (ignoring a multitude of possible lateral-thinking mechanisms including street-cleaners), and can only leave by evaporation, and that the only significant heat source is the sun. Then the total amount of water that has fallen on the surrounding area over any time period must be greater than or equal to the amount that has fallen on the area under the car(s) over that period (more than one car may have used this spot). Thus there can be less water on the surrounding area at some time only if there has been sufficiently greater evaporation on the surrounding area, i.e. the temperature of the car-area has been sufficiently lower than that of the surrounding area. This must be due to the car-area receiving sufficiently less sun than the surrounding area, and this by assumption means that a car has been parked on this spot at some point shading the ground beneath it.
Relative to any period of rainfall then, a period in which a car was parked there must be either before, during, or after the rainfall. After corresponds to @MatthewJensen's solution (the car shades the wet asphalt from the sun while the surrounding asphalt dries), before corresponds to my solution above (the car shades the dry asphalt, so that the surrounding asphalt dries more quickly after a short rain), while the car being parked during the rainfall does not add anything new to the solution (as during these times the surrounding asphalt receives at least as much water).
The true answer thus could be a combination of these two mechanisms (there may be multiple drizzles and multiple cars), and these seem to be the only two physical explanations with the assumptions we have detailed. Of course, this does not exclude unusual lawn sprinklers or sneaky OPs with watering cans...
Without such tight constraints on possible solutions, the open-ended explanations for a rectangular wet area on asphalt are essentially infinite. These include:
The 'wet patch' is actually grey paint.
After a period of rain, a magic carpet was parked above the asphalt, and this area was in its shadow.
There is currently a square cloud above the parking lot, and this is its shadow.
A long wide roll of wet carpet was left on the pavement.
An inflatable pool was sitting in the parking lot.
The two square wet spots were the footprints of an enormous square-footed robot that just walked through the lake.
Although these ideas perhaps highlight the problems with open-ended real-world puzzles like this, I admit that the rain-fell-on-the-cold-asphalt-where-a-car-had-been explanation seems the most likely to me