The tensioner pulley basically freewheels when the AC is off. When you turn it on, you put a load on it. Sounds to me like you may have a bad tensioner pulley bearing. Easy to change. If you hand turn it without the belt on, you can feel a bad bearing. If it's smooth, it's probably your AC clutch.
1989 Blue LX Hatchback
2001 Red SVT Cobra Convertible (Phoenix)
2002 Black/Red GT (Ginger)
2011 Red Candy Metallic V6 (Manfred)
2016 Magnetic Metallic GT (Susie II)