@oristarA,
Distantly--Margaret Tudor, the daughter of Henry Tudor (King Henry VII) and Elizabeth of York was married off to King James IV of Scotland, James Stuart. His grandson, James VI of Scotland (son of Mary, Queen of Scots), became King James I of Englnad upon the death of the last Tudor monarch, Queen Elizabeth. His daughter (James VI & I), Elizabeth, was married to Frederick V, the Elector Palatine.
Known as Elizabeth of Bohemia, she had a daughter, Sophia, who was married to Ernest Augustus, the Duke of Brunswick, and the son of Sophia and Ernest Augusuts was George, the Elector of Hanover. Although there were dozens of Catholic relatives of Queen Anne (Anne Stuart, granddaughter of King James I of England), the Parliament had passed an act barring Catholics from the succession to the throne. When Queen Anne died (1714) without an heir, George, Elector of Hanover, became King George I. He was succeeded by his son and grandson, both Georges, and the grandson, George III had many sons, one of whom, the Duke of Kent, had a daughter, Victoria. George III was succeeded by his son George IV, nnd George IV was succeeded by his brother, William IV. When William died in 1837, he was succeeded by his niece, Victoria. It isn't necessary to go into the marriages, but the current monarch, Elizabeth II, is directly descended from Queen Victoria.
So, the answer is yes, Elizabeth is a distant relation to King Charles I, but she is not descended from him--she is descended from the father of Charles I, James VI and I.