How long does it usually take for a shoulder rotator cuff sprain to recover?

It does not: A rotator cuff sprain is defined by a tear of the rotator cuff. Once a rotator cuff tears, the body is unable to heal the tear without a repair, in which to ends are brought back together. A rotator cuff strain is defined by an injury of the rotator cuff that may recover over 4-6 weeks once the initial injury calms down and muscle starts to function again.

About 6weeks: Rotator cuff strains usually heal in about 6weeks. If pain and dysfunction persists it may indicate a more involved problem. See your shoulder or sports medicine specialit if that happens.