Don't do that! If you rinse it, you have to wash it. Tap water is loaded with calcium carbonate that will leave water spots on your paint. You can't mechanically dry a car that hasn't been hand washed without installing swirls or scratches, as you will be pushing the left over dirt around with your drying towel.
Best thing to do is either get a good sealant topped by a wax on your paint ( or a coating). Then, after it rains, your car should be fine... For the most part, rain won't leave traditional hose/sprinkler style water spots that can etch paint. Unless of course you live near some place where there is nasty acid rain or industrial fall out. Also, keep up with maintenance washes. This will help keep the car clean and limit contaminants from bonding to the paint long term. Rain isn't as bad for your paint as you think, a lot of time hose water left to dwell or dry on paint can be worse!
If the car is clean and protected, there should be only minor water spots left after the rain.