Yes, it is possible to make money betting on Call of Duty. Firstly, you need to pick a sportsbook website that is legal in your country/state or seek an offshore one. You might need to provide your identification and proof of income to register on most reputed sportsbooks websites to register an account. The legal age for gambling can vary depending on the laws of where you live. Pretty much every sportsbook website will have a minimum age limit requirement of 18 years, if not 21.
While not as big of a giant as some other Esports, Call of Duty has a very active and passionate fanbase that makes Call of Duty one of the biggest Esports franchises. There are plenty of sportsbooks to be found that provide wagers for Call of Duty tournaments.