If a person is pregnant and she smokes, can the unborn baby get cancer from the smoking?

No, birth defects. Smoking during pregnancy is not known to cause cancer in the unborn, but it causes many complications of pregnancy, and in the newborn. This can cause premature rupture of membranes (prom), placenta previa, abruptio placenta, ectopic pregnancy, premature birth, and pregnancy induced hypertension. In the newborn, it can cause low birth weight, sudden infant death syndrome (sids), and others.