If you injured your rotator cup by playing tennis can you continue playing and how would you repair the rotator cup?

You need to have it evaluated to determine how bad it is. Pain alone is not enough of a diagnostic to determine if it needs surgery. Talk to your doctor. Yes, talk to your doctor; however just to give you hope. Les Paul, the father of the electric guitar, was in a car wreck and severly injured his right arm. He had two choices. Have it set so it would always be straight or have it set so it would always be bent at the elbow. He chose bent at he elbow so he could continue to play. The last I heard he is way up in his 80's and plays every Monday night at a place in NYC.