No. Sports betting is not legal in Ohio, but that could change as soon as 2020. Both the House and Senate have submitted bills that would legalize sports betting, though they take different regulatory approaches.
One of the bills gives sports betting control to the Ohio Lottery Commission, who would then dish out licenses to mobile and retail sportsbooks. The other bill gives power to the Ohio Casino Control Commission with a smaller tax rate.
Having to decide who will run sports betting in the state is an issue that could take some time and while sports betting in Ohio appears inevitable, it likely won't be available to residents until 2021. It also doesn't help that Ohio's public and private schools are opposed to betting.
Until then, Daily Fantasy Sports and horse racing betting are legal. Of note, auto-drafting and proposition-style fantasy contests are prohibited. Ohio passed a fantasy sports bill in 2017 and additional 2019 regulations banned prop-style contests like those from Monkey Knife Fight.