She made seven voyages for the British East India Company (EIC) between 1786 and 1802 before she was sold for breaking up.

Homeward bound, she crossed the Second Bar on 3 January 1790, reached St Helena on 15 March, and arrived at The Downs on 21 May.

She crossed the Second Bar on 26 November, reached St Helena on 24 March 1793, and arrived at the Portsmouth on 9 June.

[3] The British government held Rockingham at Portsmouth, together with a number of other Indiamen in anticipation of using them as transports for an attack on Île de France (Mauritius).

She sailed together with Boddam, Indian Trader, and Latona, and a number of other vessels, all under the escort of HMS Hector.

Rockingham reached the Cape of Good Hope on 19 September and arrived at Madras on 9 January 1797.

[2] In Bombay, the Government engaged Rockingham as a storeship supporting Major-General Sir David Baird's expedition to the Red Sea and then Egypt to help General Ralph Abercromby expel the French there.

[6] Rockingham received great damage, had to be towed off, and by 22 June she was at Jiddah, which is about 80 nautical miles (148 km; 92 mi) north-northwest of the shoal.

A letter from Jeddah dated 24 June reported that Rockingham had struck on a sunken rock and would have to return to Bombay for repairs.

She was in company with several other Indiamen: Fort William, Worcester, Airly Castle, Lord Hawkesbury, and Phoenix.