J3 Cub pilot reported a wind shift at touchdown resulted in a loss of directional control and slight damage to the aircraft from a collision with runway sign.

Narrative

I approached runway XX at ZZZ stabilized at 60 MPH with idle power applied. Aligned with the center line; I executed the round-out and touched down with a very slight bounce. After touching down; with the stick full back and into the direction of where I expected the wind to be. The nose started rotating to the left; a left yaw; with the wings level. I corrected with the ailerons into the new perceived wind direction. I applied full right rudder and some power to regain directional control. Once the rotation stopped; I pulled the power back to idle with the aircraft under directional control and firmly on the ground. I began to determine if braking or directional corrections were going to be needed to avoid obstacles. At that point I struck a runway identification sign to the left of runway XX. After which I brought the aircraft to a stopped and from the cockpit of the aircraft checked the flight controls and engine operation; all seemed to be functioning normally. I could see damage to the last few inches of the leading edge of the elevator. I taxied to a non-movement area to assess the damage further.After reviewing the weather post flight; I was able to determine that the wind shifted from approximately 250 to 160 at 7 kts during the time I was landing the aircraft.