We have investigated the effects of rotating an applied field on the exchange anisotropy in Co/FeMn thin films. When the applied field is initially along the cooling field direction, the longitudinal hysteresis loop has a maximum coercivity and the transverse hysteresis loop is flat, indicating that the exchange field is along the cooling field direction. When the applied field angle is rotated away and then restored to the original field cooling direction, the exchange anisotropy direction has changed. The rotation of the exchange field direction trails the applied field and is hysteretic. The rotational hysteresis of the exchange field direction is due to the weak anisotropy in thin FeMn layers, and decreases with increasing FeMn thickness.