King Air pilot reported safely recovering from an inflight upset when they encountered wake turbulence shortly after takeoff from a preceding A321.

Narrative

TYS tower controller had cleared an A321 for departure on Runway 5L and given that aircraft a departure heading of 070. I moved to the hold short line of 5L and was cleared for an immediate departure (without delay) on runway 5L with a departure heading of 050. I was also advised by the tower controller 'Caution; wake turbulence.' I was advised that there was a Mooney on a 1 mile final. As I began my takeoff roll; I observed that the Airbus had not yet rotated off the runway. As my speed began to increase; I observed the Airbus rotate and begin to climb. About that time; and 5000 feet (estimated) behind the Airbus; I rotated. I then noticed that the Airbus had not begun his turn to 070. At approximately 700' AGL; I activated the AutoPilot on the King Air. Simultaneous to that; I was advised to contact Departure. As I contacted Departure; I hit the wake turbulence generated by the Airbus. Even with the Auto Pilot engaged; the King Air was forced into a 60 degree right turn and was pulled to the right from its heading of 050 by at least 10 degrees. The Auto Pilot slowly corrected the deviation and turned to the set course heading. As the Pilot in Command; I should have refused the takeoff clearance and allowed more time for the Wake votices to disapate. I will henceforth refuse a takeoff clearance in future scenarios and/or veer to the opposite side of any departing large aircraft.