WASHINGTON—An online-trading startup is suing the federal government after regulators blocked its plan to let people bet on U.S. elections.

The company, Kalshi, said in a complaint filed Wednesday in the U.S. Court of Appeals for the D.C. Circuit that the Commodity Futures Trading Commission was “arbitrary, capricious and otherwise contrary to law” when it rejected the proposal to launch a market for derivatives tied to results of congressional elections.