Ropner was born in Magdeburg in Prussia in 1838. Both his parents died of cholera in 1848 and young Robert went to sea. Finding himself unable to cope with rough weather, Ropner arrived in West Hartlepool, with little English and little money. He worked at first in a bakery and married a baker's daughter. In 1859 he became a junior clerk to a local colliery fitter and coal exporter. This was at a time when the Baltic timber trade was flourishing and when wooden ships were giving way to iron steamships. West Dock had been opened in 1847. In 1860, Ropner joined Thomas Appleby's firm and in 1866 became a full partner in the firm which then became Appleby, Ropner and Co. In 1868, his first custom-built ship, a steamer with sails, was built by Denton Gray.
Ropner set up independently in 1875 as R. Ropner and Co. and soon had the biggest fleet of steamers in West Hartlepool, which developed into the largest in Britain and the world. Ropner was a pioneer of the cargo-tramp, the ship which became the basis of world trade. In 1888, Ropner bought the shipbuilding yard of Pearse, Lockwood and renamed it Ropner and Son, Shipbuilders. The yard built some 60 ships before 1914 and by 1895 had become the third largest shipyard in Britain.
Ropner was mayor of Stockton in 1893 and served as the town's MP from 1900-10. He was knighted in 1902. He lived at Preston Hall, now the museum.