Was Mary I related to James I?

Yes, they were both descendants of King Henry VII of England.

Mary I was the daughter of King Henry VIII, son of Henry VII, and his first wife, Catherine of Aragon.

Margaret Tudor, daughter of Henry VII (and, therefore sister of Henry VIII), married King James IV of Scotland.

The son of James IV and Margaret became King James V of Scotland.

James V was the father of Mary, Queen of Scots, and her son became first James VI of Scotland and then James I of England.