No. When you're in a calorie deficit, your body must burn fuel to make up for that deficit. That fuel can be muscle or fat. When you lift weights, you are signalling your body not to burn muscle, and to burn fat instead.
Your body will not create new muscle in a deficit. That would simply be counterproductive, using up more calories and creating an even bigger deficit.
The purpose of lifting is to trigger body recomposition. Instead of losing both fat and muscle as you lose weight, lifting shifts the balance so you burn more fat and less lean muscle. That is the real purpose of lifting on a cut: to retain the muscle you have, so proportionally speaking, you are more muscular.
Also, while you won't build muscle on a cut, you can gain strength. And lots of it. These strength gains are due to improved CNS functioning and muscle utilization rather than added muscle mass. You gain strength by way of your body learning how to lift weights better.