The zero-fuel aircraft arrived in Dayton at 21:56 local time (01:56 GMT) having flown from Tulsa, Oklahoma.
The 1,113km journey took pilot Andre Borschberg about 16 hours to complete, a relatively short hop for the plane.
Solar Impulse is aiming to get to New York in the next couple of weeks before it crosses the Atlantic - the last big leg in its global endeavour.
To complete the circumnavigation, the aeroplane needs to get to Abu Dhabi in the United Arab Emirates where the journey started in March last year.
As well as setting new aviation milestones, the stated purpose of the project is to demonstrate the capability of clean technologies.
The plane gets all its energy from the sun, captured by 17,000 photovoltaic cells on its top surfaces. These power the craft's propellers during the day but also charge batteries that the vehicle's motors can then call on during the night.
The craft is wider than a 747 jumbo jet but weighs just 2.3 tonnes. Low flight speed means mission legs can take several days and nights of continuous flight.
The pilot is permitted only catnaps of up to 20 minutes, and the cockpit is little bigger than a public telephone box.
LEG 1: 9 March. Abu Dhabi (UAE) to Muscat (Oman) - 772km; 13 Hours 1 Minute
LEG 2: 10 March. Muscat (Oman) to Ahmedabad (India) - 1,593km; 15 Hours 20 Minutes
LEG 3: 18 March. Ahmedabad (India) to Varanasi (India) - 1,170km; 13 Hours 15 Minutes
LEG 4: 18 March. Varanasi (India) to Mandalay (Myanmar) - 1,536km; 13 Hours 29 Minutes
LEG 5: 29 March. Mandalay (Myanmar) to Chongqing (China) - 1,636km; 20 Hours 29 Minutes
LEG 6: 21 April. Chongqing (China) to Nanjing (China) - 1,384km; 17 Hours 22 Minutes
LEG 7: 30 May. Nanjing (China) to Nagoya (Japan) - 2,942km; 1 Day 20 Hours 9 Minutes
LEG 8: 28 June. Nagoya (Japan) to Kalaeloa, Hawaii (US) - 8,924km; 4 Days 21 Hours 52 Minutes
LEG 9: 21 April. Kalaeloa, Hawaii (US) to Mountain View, California (US) - 4,523km;  2 Days 17 Hours 29 Minutes
LEG 10: 2 May. Mountain View, California (US) to Phoenix, Arizona (US) - 1,199km; 15 Hours 52 Minutes
LEG 11: 12 May. Phoenix, Arizona (US) to Tulsa, Oklahoma (US) - 1,570 km; 18 Hours 10 Minutes
LEG 12: 21 May. Tulsa, Oklahoma (US) to Dayton, Ohio (US) - 1,113 km; 16 Hours 34 Minutes
Solar Impulse has landed in the US state of Ohio following the 12th stage of its circumnavigation of the globe.