What poisonous element is used in medicines and also in rat poison?

Warfarin. It is a white crystalline compound that is used to kill rats and other rodents.

Warfarin is also used as a medicine for people, to make their blood thinner so that it does not coagulate so easily.

Other answers

Bromadiolone is also found in rat poisons and is composed of bromine, a poisonous element.

Ipratropium bromide is a medication used as a bronchodilator - it assists breathing for patients with lung damage or Asthma-type ailments.

Note that warfarin, bromadiolone, and iprtropium bromide are compounds rather than elements.

A common element used in rat poison is Arsenic, although there are other components such as zinc phosphide, bromethalin, and cholecalciferon.

Thallium is higly toxic, is used in rat poison (though it's currently banned in the US) and a radioactive form (thallium-201) is used in cardiac testing.