He was born near the town of Beaufort West, the son of Hendrik Janse van Rensburg and his second wife, Martha Magdalena Oosthuizen. Van Rensburg married Elizabeth Maria Jacoba Du Plessis (31 October 1819 - 6 August 1895) in 1838.
Initially he travelled with a party of Voortrekkers to Natal, and was one of the party of van Rensburgs who survived an attack by a group of Zulus at Rensburg koppie (Rensburg hill). He subsequently travelled to the Transvaal and settled on a farm in the Rustenburg area in 1848.
Van Rensburg was elected as a member of the South African Republic's (ZAR) Volksraad (People's Assembly) in 1850, a post which he held until June 1855. During this period there was a major political conflict between the ZAR's First President and writer of its constitution, Marthinus Wessel Pretorius, and its Commandant-General, Stephanus Schoeman, who rejected the constitution. Van Rensburg supported Schoeman and in return the latter appointed van Rensburg as a provisional commandant. Van Rensburg subsequently represented Schoeman in negotiations with Pretorius's faction. In 1858, when Schoeman fell ill, Van Rensburg was appointed as acting Commandant-General.
In February 1860, during Pretorius's absence, the Volksraad offered Van Rensburg the post of State President, which he refused. Following substantial political maneuvering, Van Rensburg was elected as the Second President of the ZAR in April 1863. However, Van Rensburg refused to be sworn in and a second election had to be held. During this election Van Rensburg received 1,106 votes and Pretorius 1,065; Van Rensburg accepted his election this time and he took his oath of office on 23 October 1863.
Pretorius's supporters did not support the results of the election and what amounted to a civil war broke out. When the fighting came to a halt in January 1864 another presidential election was held and Pretorius was re-elected; he was sworn in on 9 May 1864. Van Rensburg subsequently returned to his farm near Rustenburg, where he died and was buried shortly afterwards. However, in August 1974, Van Rensburg and his wife were disinterred and reburied at the Heroes Acre cemetery in Pretoria.