Can you wait for a few weeks after a rotator cuff is torn to have it repaired?

Yes. This is far from an emergency and although it needs to be addressed, the timing does not need to be urgent. Anytime within several months should be sufficient to produce good results. See a board certified orthopaedic surgeon, who performs arthroscopic rotator cuff repair.
Yes. You can wait a few weeks to have a rotator cuff repaired, but you should maintain the range of motion to avoid stiffness and adhesive capsulitis (also known as a frozen shoulder). Over time, the muscles of the unrepaired tendons will start to atrophy and turn fibrotic, but this won't happen in just a few weeks. Also, not all tears need to be repaired. Many can be managed with rehab alone.