Rhode Island—one of eight states with active sports betting laws—could soon expand its sports betting regime to the internet.

Senate President Dominick J. Ruggerio (D) introduced a bill Jan. 16 that would allow online sports betting. The state currently allows the bets at two brick-and-mortar casinos and retains 51 percent of sports betting revenue. The proposed law would set the same tax rate for online bets.

“Expanding to mobile gaming would provide a convenient option for those wishing to enjoy...