扌 is the left-side form of 手 (hand). Kneading, rubbing and massaging are all manual actions, so 揉 takes the hand radical without question. Compare 搓 (rub between hands), 按 (press), 抚 (stroke), 摩 (massage).
柔 (róu) supplies the sound, unchanged. The semantic echo is strong — kneading dough or muscles softens whatever you're working, so 揉 is literally the hand-action of making things 柔 (soft). Same phonetic: 蹂 (trample), 鞣 (tan leather).
