There was no noise before my tires were rotated.

That's typical of a worn upper strut mount. It can be aggravated by simply hoisting the car up to rotate the tires. Hoisting it didn't CAUSE the problem, it just made it noticeable.

Reach over the front tires and lightly wrap your fingertips over a coil of the coil spring, then have a helper slowly turn the steering wheel. You should feel the spring turn smoothly with the wheel. If you feel it wind up then suddenly pop free and turn, or it feels rough, you identified the cause of the noise.