A shift range control apparatus is applied to a shift range switching mechanism that includes a rotation member including multiple recesses, and an engagement member that positions the rotation member by engaging to the recesses. The shift range control apparatus controls a motor of a shift actuator connected to the rotation member to switch a shift range. The shift range control apparatus includes a rotation speed detection section that detects an output shaft rotation speed corresponding to a rotation speed of an output shaft of the shift actuator, and a movement determination section that determines that an engagement portion of the engagement member has relatively moved to a bottom of one of the recesses of the rotation member when the output shaft rotation speed is equal to or lower than a predetermined value during switching of the shift range.