The short answer to that is no, Meghan Markle could not become queen, but she could, however, possibly become a queen consort.
Succession to the British throne is regulated by descent (hence why Queen Elizabeth’s son, Prince Charles, is next in line). In other words, those who marry into the royal family aren’t included in the line of succession. Yep, that means that even Kate Middleton won’t become the Queen of England when her husband assumes the throne, but will instead hold the title of Queen Consort.
But the chances of Meghan Markle even obtaining the title of Queen Consort are pretty slim. That’s because her husband, Prince Harry, would have to be appointed king and he’s currently fifth in line for the throne (after Prince Charles, Prince William, Prince George, Princess Charlotte and Prince Louis).
Sorry, Meghan, looks like you won’t be adding “queen” to your title anytime soon. But hey, we’d settle for “duchess” any day of the week.